Dissertation Voting Systems

8/4/2019 Dissertation Voting Systems

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Assess the legitimacy

of vote countingmethods in modern

democratic electoralsystems

0818526


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Abstract

By analysing three concepts of legitimacy in vote counting, I intend to prove that the

Alternative Vote (AV) system is the most legitimate counting method overall. Internal

Legitimacy concerns the inner mechanics of a counting system on these criteria simple

systems are the best. Consent Legitimacy refers to whether the outcome of a count can

be reasonably said to derive from the approval of the voters this is shown to require

permissive rather than restrictive ballot structures. Formal Legitimacy is how well a

system reflects the plausible behaviour of people in simple voting dilemmas on this

front the procedures of AV are best at such reflection. In so far as they are necessarily

problematic for systems, the issues of Formal Legitimacy are given most weight,

followed by issues in Consent Legitimacy which are contingentlyproblematic. The best

system based on these criteria is the Alternative Vote.

Word Count: 9001


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Table of Contents

Abstract........................................................................................2

List of tables and figures.........................................................4

List of abbreviations................................................................5

Introduction................................................................................6

Chapter 1: Internal Legitimacy..........................................10

Chapter 2: Consent Legitimacy..........................................17

Chapter 3: Formal Legitimacy............................................28

Conclusion.................................................................................42

Bibliography.............................................................................46


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List of tables and figures

Figure 1: Framework of an electoral system.........................................................................8

Figure 2: Example candidate shares by preference..........................................................14

Figure 3: Effective votes in Warwick Students Union presidential election...........26

Table 1: Example election using a categorical ballot structure....................................11

Table 2: Example preferential election susceptible to monotonicity violation......13

Table 3: Example election using non-compulsory ballot structure............................22

Table 4: Borda counts.................................................................................................................23

Table 5: Revised version of table 3 election with compulsory ballot structure......24

Table 6: Preferences of friends at the cinema, based on the original position.......30

Table 7: Candidate victory probabilities under different voting methods...............30

Table 8: Preference stating dilemma.....................................................................................33

Table 9: Example election with ambiguous outcomes.....................................................35

Table 10: Voting dilemma..........................................................................................................36

Table 11: Table 10, Based on expectation that Ernest will defect...............................38

Table 12: Voting dilemmas based on election in table 9.................................................40


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List of Abbreviations

AV: Alternative Vote

HP: Harry Potter (table 6)

IRV: Instant Runoff Voting

LR: Lord of the Rings (table 6)

SMP: Single-Member Plurality

TS: Toy Story (table 6)


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Introduction

Given the vastness of the literature regarding voting systems and public choice fields

upon which this essay is primarily based I intend to begin by defining my own

framework by which the fields can be categorised, and then localising my own project

within. It should be noted that to comprehensively address the question would require

exploration of all the categories within the framework, a task which is beyond the scope

of this essay. To proceed given limited resources, I therefore hold all variables not

related to the topic upon which I focus as fixed, and for the purposes of this particular

investigation I shall cast aside any issues outside of my category of focus. This will lead

to a conclusion that is limited to the variables dealt with, and so any scope for

generalisation will be limited.

Of previous efforts at defining a framework for assessing electoral systems, the most

resilient has proven to be that set out by Douglas Rae and utilised by Gary Cox.1 He

defines three main aspects of a voting system: the ballot structure, the electoral formula

and the district magnitude, and introduces supplementary variables to apply to each. A

similar though more comprehensive approach is taken by Katz who widens the areas in

question, although he attaches to this a warning that the definition cannot become too

broad.2

My own framework owes much to the work of Rae, however I expand on it in a number

of ways. First of all, while Raes framework confines him to covering the translation of

votes into seats, my own expands this to cover the translation ofpreferences intopower.

1

Rae, D: The Political Consequences of Electoral Laws (1971), Cox, G: Centripetal and Centrifugal Incentives(1990)2

Katz, R: Democracy and Elections (1997), p.107


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While both votes and seats play a vital role within this framework, I place them as

merely intermediate factors rather than origin and destination as offered by Rae.

Secondly, while Rae and Katzs work is primarily descriptive, my own is designed to

accommodate a closely normative nature of assessment. In this essay the object of

normative analysis will be legitimacy.

The structure is illustrated in figure 1 below. There are six objects of analysis:

Individuals, the preferences of those individuals, the votes they cast to reflect their

preferences, the local outcomes once those votes are counted, such as the election of a

local representative to a legislative body, the global outcomes such as the

apportionment of seats in a parliament, and the decisions arrived at by the body via

some further voting procedure. From these categories emerge fiveprocesses by which a

voting system connects them together: Preference Formation concerns the process by

which individuals come to acquire their preferences in the first place. Preference

Translation refers to the mechanism used to yield quantifiable data from such

preferences, which can subsequently be counted and aggregated. Alternately it can be a

qualitative mechanism, for instance a deliberative process designed to allow individuals

to trade priorities and preferences as if they were commodities. Vote Counting concerns

the process by which the data from votes is counted and by which a result is generated.

Vote Aggregation is similar in structure to vote counting but has a global rather than a

local scope, concerning how multiple local results generate a resultant distribution of

seats in a legislature or the relative voting power of each elected representative. Finally,

Decision Making refers to the way in which social choices and outcomes are derived

from whatever representative body has resulted from the previous steps.


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This framework has been so formed in order to accommodate an analysis oflegitimacy

at each stage. The intended analytical approach is to suggest issues of legitimacy that

are relevant to each stage, judge voting concepts on how well they deal with each issue,

and conclude what criteria are necessary for a system to maximise legitimacy in the

appropriate sense. Ultimately, the system that leaks the least legitimacy across the five

stages can be logically judged to be the most legitimate system.3

This essay is concerned primarily with the third stage of the electoral process: Vote

Counting. Various vote counting concepts will be assessed against three types of

legitimacy that relate to the issues of vote counting: Internal Legitimacy, Consent

3

In reality very few systems are concerned with processes 1) and 5), the formation of preferences is taken asgiven and the power output assumed as fair so long as the direct input, the legislative assembly, is fair in

composition. Both stages are nevertheless included to highlight the rashness of these two assumptions.


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Legitimacyand Formal Legitimacy. Each section will proceed by outlining the legitimacy

concept under discussion and the requirements it places upon systems aiming to be so

legitimate. After discussing how systems cope with the difficulties, the sections will

indicate which systems are to be preferred in a normative sense based on the criteria

outlined at the start. A final conclusion will then weigh the importance of each type of

legitimacy and deliver an overall verdict as to which system fares best overall.


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Chapter 1: Internal Legitimacy

Internal legitimacy is based on the logical mechanics of a vote counting system. It is

concerned with how the elected outcomes of an election derive logically and entirely

from the preferential inputs. A system can fail either because its outputs do not

correlate with its inputs or because it uses data other than preferences. For instance, a

system that is not monotone, i.e. it allows for situations in which increased support for a

candidate ceteris paribus can cause that candidate to lose, is not internally legitimate

because the output is not logically derived from the input.4 Similarly, a system that uses

some other input than the preferences of all voters, such as a dictatorship or random

chance, is not entirely preferential in basis and thus fails on internal legitimacy in this

sense.

No voting system can be perfectly internally legitimate because of the possibility of

stalematescircumstances in which the mechanics of the system have failed to produce

a decisive result.5 Invariably, such stalemates are broken using some form of random

chance such as the toss of a coin, but in the strictest sense this is not a preferential input.

Thus all systems suffer from this imperfection and the only relevant dimension of

analysis is the likelihood of such a situation arising. Other than this all voting systems ,

in so far as they are not dictatorial and treat votes strictly equally, are entirely based on

preferential inputs and thus are untroubled by this aspect of internal legitimacy. Thus

the only required areas of analysis are the logical coherence of the voting mechanism

and the probability of stalemates.

4In this sense logic depends on positive relationship between inputs and outputs. In non-monotone systems

this relationship can be negative, i.e. an increased input can yield a decreased output5Even if there are an odd number of voters, any could abstain or fail to turnout, meaning an even number is

invariably a possibility, and thus a tied result a possibility also


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Probability of Stalemates

The probability of a stalemate arising is dependent on four factors: The number of

voters, the probability that the number of voters is odd, the closeness of the contest, and

available tiebreaking data. The first three factors are externalities and do not strictly

depend on the voting system used.6 However the availability of tiebreaking data

concerns the amount and complexity of data taken in the first place, which depends

entirely on the ballot structure. Categorical structures used by Single Member Plurality

(SMP) and Approval Voting inevitably have limited data compared to preferential

structures in which up to every possible preference a voter may have is stated.7 Such a

limitation is exposed by table 1. Here, SMP suffers from its relative lack of data, since the

only way to break the tie between A and B is to use random chance a step-down from

ideal legitimacy. Approval Voting has more detailed data regarding the number of votes

cast per ballot paper, but this is irrelevant for breaking a tie since the number of

approval votes cast on a ballot has no effect on the weight of the votes cast on that

ballot.

Table 1: Example election using a categorical ballot structure

Candidate Votes

A 2

B 2

C 1

6

Some voting systems may have a propensity to affect the closeness of a contest, but this variable is tooheavily dependent on external factors to be useful to this analysis7The terms categorical and preferential ballot structure are taken from Rae (1971)


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Conversely, preferential systems are capable of using further data to attempt to break

the tie. The Alternative Vote (AV), for instance, would eliminate candidate C from the

ballot and examine its second preference. Such a mechanism is by no means a

guaranteed tiebreaker since no further preference could be stated or the number of

redistributed votes could be even, raising the possibility that a tie could still occur after

transfers.8 Nevertheless, the potential for a tiebreaker exists under preferential forms

whereas under categorical forms such potential does not exist. Thus preferential

systems are more legitimate than categorical systems in that they are more likely to

deliver a complete result.

Monotonicity

The monotonicity problem is a significant concern in terms of logical consistency. Only

runoff systems are susceptible to this problem, in particular the Alternative Vote. AV is

one of the few non-monotone systems in other words increased support for one

candidate can cause that candidate to lose. In table 2, the AV winner is A with a margin

of 13 to 8 against C. However if all ofDs voters were to switch to A, B would be allowed

into the final round ahead of C, and would be victorious by a margin of 11 votes to 10

against A. Thus the nature of the problem is not so much that As votes increase or that

Ds votes decrease, but that C is displaced into third place, allowing a stronger candidate

to face A and emerge victorious.

8Although under compulsory preferential voting such as that used in Australia, the problem of no further

preferences does not exist


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Table 2: Example preferential election susceptible to monotonicity violation

Voters 1stpref. 2nd pref. 3rd pref. 4th pref.

7 voters A B C D

6 voters B A C D

5 voters C B A D

3 voters D C B A

The problem highlights a stark contradiction in the way AV treats preferences. On the

one hand, advocates argue that AV treats preferences equally, and that, in a count, if

ones first preference is eliminated then ones second preference will be counted equally

alongside other voters first preferences. As a corollary, the principle of majority is

based on such equal treatment since, in the absence of a first-round majority, a

candidates majority after all rounds are complete will be a mixture of first and

secondary preferences. This necessitates that the first and secondary preferences are

counted equally and not weighted differently; otherwise AV cannot guarantee majority

support for the victor. Consider the case in figure 2. A has 50%-1 and B has 25%+1 of

the vote, thus C is eliminated and all of his preferences are transferred to B, giving B a

50%+1 share and victory. In this case, anyweighting given to first preferences at the

expense of second preferences will result in the defeat of B since it would diminish his

share to beneath a majority. Hence AV requires equal weighting of preferences in order

to function in the intended sense.


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Figure 2: Example candidate shares by preference

On the other hand, the monotonicity problem demonstrates that AV does not treat

preferences equally during the elimination process. Because it bases elimination on first

preferences, even a Condorcet winner could be defeated if he or she acquired too few

first preferences. In the example from table 2, B was the Condorcet winner, yet was

usurped by C in the second round and was thus eliminated early on. If the system were

incapable of eliminating the Condorcet winner, the problem of monotonicity would not

arise since the same winner would reach the final round under any circumstances and,

being the Condorcet winner, would invariably win the final round. AVs problem

therefore stems from a combination of maintaining preference equity when

redistributing preferences and prioritising first preferences when eliminating

candidates. Thus AV fails on logical consistency not only because of non-monotonicity

but also because of inconsistent weighting of preferences. That it is a unique failing is

damaging in itself, however, like the probability of having tiebreaking information, the


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problem is tempered by the likelihood of such a situation in which the problems are

exposed arising. Research by Lepelley, Chantreuil and Berg has shown that the

probability of a violation occurring is low but not negligible.9 So the lack of internal

legitimacy suffered by AV is certainly a problem but is probabilistic in nature.

Conclusion

This section has discussed two key issues of internal legitimacy: completeness and

consistency. All vote counting methods are incomplete to some extent since they are all

susceptible to stalemates, and hence requiring random chance as a tiebreaking

mechanism. Indeed, the only ways of inevitably avoiding such an outcome involve

compromising completeness in other senses, such as arbitrarily controlling the number

of voters. However, counting systems can be differentiated in how well they provide

tiebreaking mechanisms internally, such as examining more preferences where

appropriate. Investigation revealed that the mere complexity of a voting system renders

it more effective in this regard. In terms of consistency, plurality systems are both

perfectly consistent and unambiguous in how the candidates are ordered from given

preferential inputs. Majoritarian systems however pose problems the Alternative Vote

fails the monotonicity test which is a major failure of positive correlation between

preferential inputs and winner outputs. Other majoritarian systems pose additional

problems such as ambiguous ordering of candidates after transfers have occurred.

Hence, plurality systems are inherently more consistent given their lack of ambiguity

and avoidance of monotonicity problems.

This section therefore prescribes complex systems for completeness and plurality

systems for consistency. Since these are very much in contradiction, more weight is

9D. Lepelley, F. Chantreuil and S. Berg: The likelihood of monotonicity paradoxes in run-off elections (1996)


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given to the consistency criterion since, while a lack of completeness can yield a

candidate who is only the joint winner, a lack of consistency can yield a winner who has

won by virtue of the monotonicity violation a more concerning outcome. Hence, in so

far as internal legitimacy is valued, plurality systems are to be preferred.


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Chapter 2: Consent Legitimacy

Consent-based legitimacy is primarily concerned with the concept ofmandate. It is often

said that a mandate results from one candidate emerging victorious from a voting

procedure but this is imprecise. Katz instead states that the idea of a mandate in

liberal democracies derives from unanimous consent:

The electoral system must be perceived as sufficiently fair that those who areunhappy with the outcome of a particular election nonetheless accept the

winners mandate as legitimate.10

Even though most voting systems require only a majority or plurality of support for a

winner to result, all systems require unanimous or near-unanimous acceptance of the

result itself. A representative does not only represent those who voted for him or her,

they represent all voters thus all voters must at least accept the means by which the

result is arrived at.11 It is thus not enough for a candidate to win in order to achieve a

perfect mandate that candidate must command consent from all the electors after the

result has been declared. Systems can be judged against this standard by assessing to

what degree the winning candidate has garnered consent from the electorate. Since

informed consent for a process necessarily entails consent for the outcome of that

process, the relevant area of analysis is whether informed consent can be reasonably

assumed.

The grounds for reasonably assuming informed consent essentially embody the quality

of voter consultation. If consultation is adequate, voters have no grounds to question

10Katz (1997): p.35

11

The point that representation is universal regardless of how votes were cast is dealt with by the PolicyExchange Think Tank in their attack on the wasted votes concept: R. Mcllveen: The Alternative Vote The

system no-one wants (Oct 2010), p.15/16


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the outcome insofar as it is derived from their declared preferences. It is inadequate if

there exists a situation in which, given the same voter preferences, a majority of voters

can reasonably disapprove of the outcome. Hence, the means by which the quality of

consultation can be judged is via the approval criterion. If a voter has in some way

expressed an approval for a candidate above the available alternatives, he or she has

surrendered the right to disapprove of an outcome in which that candidate is victorious

against the same alternatives. Adequate consultation will always succeed in yielding

outcomes that are approved by a majority of voters.12 The approval criterion is thus the

basis by which three concepts:preferences, freedom and the nature of consentare

hereon evaluated.

Preferences

First preferences are the only preferences that unambiguously imply approval for the

chosen candidate. As a corollary, last preferences unambiguously imply disapproval for

the chosen candidate.13 By stating a first preference, a voter is in fact able to express a

number of preferences depending on how many candidates are in the contest. With

three candidates, a first preference states two things: a preference for the chosen

candidate over the first alternative candidate and a preference for the chosen candidate

against the second alternative.14 When only a first preference is stated, the function of

expression is thus:

e = n-1 [where e is the degree of expression and n is the number of candidates]

12This is one principle behind the Approval Voting system itself see Brams and Fishburn (1983)

13The rationale behind approval voting is that voters cast effective rather than merely expressive votes, hence

they are not expected to mark all or none of the available options, but differentiate somewhere intermediately14By expression is meant the expression of inequality rather than the expression of indifference, which in

vote counting terms renders the vote null


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As long as there are at least two candidates in the race, the first preference will thus

always state at least one preference for the chosen candidate above any other option. As

a result, any election that yields a majority for one candidate on first preferences has

proven that candidate is approved of by a majority of voters, and thus there are no

grounds for reasonable dissent. Since no voting system is capable of guaranteeing a

majority of first preferences as such, no voting system benefits from this criterion of

consent legitimacy.15

Hence the lack of first-preference majority opens up the possibility that the plurality

candidate might not command majority approval. Thus any system that stops at mere

plurality when deciding a winner suffers from the problem of majority disapproval. The

possibility is embodied in the inability of some plurality systems to guarantee defeat of

the Condorcet loser, if it exists. If a candidate is a Condorcet loser, they are defeated in

every possible pairwise comparison in the contest. As such, any of those candidates

would garner majority approval if the only alternative was the Condorcet loser. If the

Condorcet loser exists in the first place, it follows that a majority of voters have

expressed a comparative disapproval of that candidate. Thus, it is reasonable, based on

the approval criterion, for voters to complain if the Condorcet loser is declared the

winner. So systems such as SMP, which cannot guarantee defeat of such a candidate,

cannot aspire to have consent legitimacy when there is no majority for any one

candidate.

The only way to avoid the problems of SMP is to enhance the quality of voter

consultation. SMP limits voters to stating a first preference, and so allows a latent

15

Only be restricting the number of candidates to two can a system guarantee majority approval, save for thesmall chance of ties. This restriction is however deemed arbitrary and against the democratic principles that

are embedded assumptions in this essay


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Condorcet loser to win by virtue of the fact that is does not properly test how preferred

the candidate is. So the formula of expression in [p = n-1] is too restrictive. Preferential

systems offer a potential remedy to this restriction. By allowing not only primary but

secondary preferences to be stated, the voters scope of expression is enhanced. When a

number of preferences are possible, the function becomes:

e = pn - [where e is the degree of expression, p is the number of

preferences listed and n is the number of candidates]

So, if there are four candidates and a voter lists three preferences, the degree of

expression is equal to six, since six things are being stated. If the candidates are ranked

A-B-C with no marking for D, then the six expressions are thus:

1) A is preferred to B2) A is preferred to C3) A is preferred to D4) B is preferred to C5) B is preferred to D6) C is preferred to D

Whereas under SMP, where only the first preference is permitted, only three things can

be stated by such an ordering:16

1) A is preferred to B2) A is preferred to C3)

A is preferred to D

The problems for SMP thus derive from how it deprives a system of the information in

statements 4), 5) and 6) above. This is problematic for this example voter if candidates

B, C or D were to be victorious in the contest. If, for instance, D were to win, this voter

would latently prefer A, B or C to have won by statements 3), 5) and 6). However, the

16The ordering is considered latent something that exists in the voter regardless of how many items in the

order are manifested by a voting system

(p2 + p)

2


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latter two statements are not permitted by SMP, and so the voter cannot express their

opinion on this matter. To claim that they have consentedto the outcome of the contest

is thus questionable since their own preferences have not been adequately consulted.

Thus, preferential systems are essential for affording voters adequate consultation and

avoiding violation of the approval criterion.

Freedom

Voting systems vary greatly on the degree of freedom they afford voters.17 For instance,

among categorical systems; SMP and Block Voting only allow voters to mark

preferences next to as many choices are there are winners to be declared, while Limited

Voting forces voters to choose fewer options than winners and Approval Voting allows

voters to mark as many or few options as they wish, regardless of the number of

winners.18 Among preferential systems; the Supplementary Vote (SV) as used in London

Mayoral elections allows voters to express two preferences, while Papua New Guineas

AV system allows three, the UKs proposed AV system allows as many or as few as

voters wish, and Australias version of AV requires all candidates to be ranked, as do

Condorcet Methods, the Borda Count, and Coombs Method if they are to operate

effectively.19 Most of these aspects of freedom affectexpression, as dealt with in the

previous section. However, compulsory voting is not merely restrictive it is actively

constrictive in that it forces voters to express their preferences comprehensively, given

every possible contingency of pairwise contests. Algebraically, in line with the formulae

of the previous section, this amounts to a requirement that p = n.

17

For an overview of how ballot structure affects voter freedom, see Farrell & Mcallister (2006), p.72518S. Brams and P. Fishburn:Approval Voting, (1983)

19See B. Grofman and S. Feld (2004) for a rare illustration of Coombs requirement in this regard


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The problem this concept highlights in terms of approval is clear: if voters are forced to

express comprehensive preferences, they are prevented from specifying a frontier of

approval. Under optional preferential systems, voters can opt not to state any further

preferences at any stage they choose to do so, in the knowledge that the lower placed

candidates will receive no approval. However, if this approval isforcedinto existence,

then the existence of a majority approved candidate is inevitable, even if, under optional

structures, no such majority would exist.

Consider the following example. In table 3 below, all of the voters have two preferences

first and second. That they only state two preferences implies that they express

indifference between the other two candidates. Given this information, A wins a

plurality. But since the approval criterion requires that a Condorcet loser be avoided,

further preferences must be examined to ensure this is not the case. Using AV as an

example preferential system, D is eliminated and his votes are transferred to C. Now B is

eliminated, having been usurped by A. However, since B only expressed a second

preference for D, her votes are exhausted, and A wins the contest by 8 votes to 5 for C.

Table 3: Example election using non-compulsory ballot structure


8 voters A B

4 voters B D

3 voters C B

2 voters D C


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Table 4: Borda counts (column-based candidates scores against row candidates)

Candidate A B C D

A 8 8 8

B 7 12 15

C 5 5 3

D 6 2 6

Table 4 clearly shows that, in the example, A is the Condorcet winner and C is the

Condorcet loser. Against any opponent, eight voters express a preference for A which,

while not being an absolute majority, is a majority of voters who chose to state enough

preferences. In the contest of A versus B, for instance, A scores 8 votes and B scores 7

votes. Candidate Ds two voters expressed indifference between A and B and thus

neither vote can be counted in the A versus B contest. Hence, A attained a majority of

valid votes.

That the system has avoided the election of C, however, is sufficient for regarding it as a

legitimate system from a consent point of view. However, now consider if the voters

were forced to state all preferences. If those new preferences emerged as they do in

table 5, a problem emerges. Now, under AV, candidate C wins by virtue of Bs voters

preferring C to A. In this situation, theformerCondorcet loser is no longer defined as

such, and the former Condorcet winner is revealed to be the Condorcet loser instead.


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Table 5: Revised version of table 3 election with compulsory ballot structure


8 voters A B C D

4 voters B D C A

3 voters C B D A

2 voters D C B A

By adhering to the approval criterion however, such a result should be regarded as

illegitimate. By stating only two preferences each, the voters were each expressing five

things about their preferences.20 Four of those expressions show that the two unmarked

preferences were both less preferred than any alternative except to each other. For

instance, As voters expressed that they preferred any alternative to C or D. This is

enough grounds to conclude that As voters disapprovedof C and D since they were

incapable of being anything other than last preferences, which are unambiguously

disapproval votes in the relative sense. If, however, any lack of preference marking is

interpreted as disapproval for that candidate, Candidate C the Condorcet loser initially

wins the most disapproval votes by garnering twelve against Ds eleven, As nine and

Bs two. Hence when a system, by coercion, forces the stating of disapproved candidates,

it allows them the possibility of winning when otherwise they would not have been able

to do so. Compulsory voting thus creates inauthentic preferences and adds them to the

count, which can distort the contest away from candidates who were genuinely

approved of. Based on this it is thus also essential that a ballot structure is non-

constrictive in order for consent to be authentically derived.

20See formula on page 20 for derivation


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That nature of consent: Express and Tacit

Perhaps the most important aspect of a permissive structure however is that it allows

for tacit consentto act as a legitimate factor and thus guarantee the creation of a

majority winner. Without this, the existence of exhausted ballots increases the

likelihood that the winner will fall short of majority support. In the above example, As

victory against C was based on a minority of approved votes only eight voters

expressed a preference for B while nine did not. However, because Bs voters were

indifferent between A and C, A won a majority of valid votes. One often-made claim by

advocates of such majoritarian systems is that they necessarily produce winners who

can boast majority support. However the terminology of the advocates claim is

misleading since the winner might not strictly command a majority of the votes cast. A

more precise term for a winner under majoritarian systems is that they command

majority acquiescence in the contest.21

A real-life illustration is provided by the 2011 Warwick Students Union presidential

election in which nine candidates competed under an Alternative Vote majoritarian

system. In the final round, Leo Boe won by a margin of 54.8% against 45.2% for Jane

Costello. However, when exhausted ballots are counted, Boes share drops to 35.5%,

with 29.3% for Costello and 35.2% exhausted ballots. Hence Boes 54.8% total was not

majority supportbut majority acquiescence. The assumption embedded in the AV

system is that the 35.2% of ballots that did not express a preference between Boe and

Costello effectively acquiesced to whatever the final result would be between the

candidates. Hence, in effect, they were transferred to both Boe and Costello. This

difference between support and acquiescence can be characterised as a difference

21See Jenkins et.al: The Report of the Independent Commission on the voting system (1998), section 81


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between express and tacitconsent. The importance of having a permissive ballot

structure here is clear: voters need to have been able to express indifference in order

for tacit consent to exist. Otherwise, only express consent derived from inauthentic

preferences can be used, which is thus inadequate.

Figure 3: Effective votes in Warwick Students Union presidential election22

In figure 3 above, the darkest-shaded areas representing valid votes and transfers,

indicate express consent for each candidate, while the lightest area represents tacit

consent. Since the exhausted ballots did not express an opinion between Boe and

Costello despite having the potential to do so, they are effectively voting for both

candidates equally.23 Hence, the total mandate, express plus tacit, for each candidate is

70.7% for Boe and 64.5% for Costello. Hence, Boes victory is legitimate from a consent

point of view since he has attained a vast majority of the voters consent. In order to

account for the fact that Costello also has a majority, albeit smaller, the relative

majorities can be taken into account to insure that Costello is not declared a legitimate

winner. In this case the shares return to the original result 54.8% for Boe and 45.2%

22

University of Warwick Students Union Sabbatical Officer Elections (2011) 23In the election there was also an option for voters to select Re-Open Nominations, indicating consent for

neithercandidate. These ballots are thus not part of this exhausted category.


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for Costello. Thus a permissive ballot structure in this sense guarantees a legitimate

majority winner.

Conclusion

In this section, preferential systems were shown to be best at allowing for adequate

expression while permissive ballot structures were deemed essential for majoritarian

systems to be legitimate in their outcomes. However, one confounding variable

Approval Voting remains since it uses a permissive ballot structure, allowing voters to

express as many or as few approvals as they wish. It also has the virtue of avoiding

undue conflation between express and tacit consent, since all counted votes in Approval

Voting are express votes. However, Approval Votings lack of allowance for tacit consent

damages its ability to deliver a legitimate outcome. For instance, the formula of

expression in Approval Voting is:

e = pn - - (n-1)

[where e is the degree of expression, p is the number of preferences listed and n is

the number of candidates]

The addition of [- (n-1)] embodies the fact that approval voting allows no distinction

between fellow approved candidates. Hence in the senses described a few sections ago,

Approval Voting falls short of allowing adequate expression. For this reason,

preferential voting under permissive ballot structures is to be preferred for consent

legitimacy.

(p2

+ p)2


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Chapter 3: Formal Legitimacy

Formal legitimacy refers to the way in which a vote counting system reflects authentic

voter behaviour. Every voting system is to some extent aformalisation of human

behaviour; for instance, systems that involve the elimination of candidates and the

subsequent redistribution of preferences effectively formalise tactical voting.2425 The

question that needs to be raised in light of this is whether such formalisation is justified.

The criterion of transparency requires that voters understand the mechanics of a

system; without such understanding they cannot be said to have authentically

consented to the result. However if a complex mechanism can be proven to be a

watertight representation of rational voter behaviour, it follows that transparency is not

thus required for formal legitimacy in such cases. A voting system can thus only be as

complex as can be justified by means of sound rational choice models. Any system that

falls short of this complexity boundary is at best inefficient and at worst insufficient,

while any system that probes beyond is arbitrarily illegitimate.

All voting systems require two formal procedures to function properly: They necessitate

the express recording of votes in a form that can be verified and counted, and they

require that a result be declared at the end of the vote counting procedure. Any

additional mechanisms employed are unique to the particular system using them for

instance the procedure of candidate elimination and preference redistribution involved

in preferential systems. The simplest system from a formal perspective is SMP, which

only requires verification of votes and declaration of a result after votes have been

24R. Mcllveen:(2010), p.2

25

Grofman (2008) covers the concept ofanalogue voting systems systems which formalise a moreconvoluted procedure, for instance the Supplementary Vote is an analogue of the Two-Round system as used

in France, although with imperfections regarding the possibility of exhausted ballots


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counted. Although every system involves some formalisation, SMP can be characterised

as a relatively informal system for this reason.

The benefits of informality are similar to the benefits for simplicity outlined in section

one: Because the system tries to do very little there is limited scope to question its

legitimacy in either an internal or a formal sense. The only grounds to question SMP in a

formal sense are to either question the validity of formal verification, of which every

system will be equally under attack, or question the validity of formal declaration, which

similarly affects all systems.26

Informal systems can thus be best analysed when compared with systems that are

formal analogues i.e. systems that appropriate actions that exist but are not recorded

under informal methods. If the formal methods can be willed as formally legitimate, the

informal methods fail on the grounds of insufficiency. Meanwhile, failure to will formal

mechanisms as legitimate automatically lends weight to the informal corollary. The

concepts of informality and formality are mutually exclusive, and analysis can be

confined to one to adequately characterise both.

The Original Position

To proceed with this analysis, a simple model of voting behaviour is required. For this, I

provide a conceptual original position in which the voters present are perfectly rational

and unaffected by extraneous variables; albeit for the sake of illustration a context will

be provided so the purpose of the decision-making is clear.Let us imagine five friends

who are going to the cinema for a night out. There are only three films being shown that

evening, each of which is equally convenient to watch in every relevant sense. We

26

The validity of declaration against preferential inputs has already been dealt with in the previous sections.This section is designed to deal with factors unique to formal legitimacy rather than factors supplementing

areas already covered


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assume that each friend has distinct preferences between the films, and that there are

no confounding variables such as power dynamics or special relationships between the

friends. Finally, each of the five friends has an absolute preference to watch the same

film as the other four, thus lending impetus to a single winner outcome. Essentially, the

only relevant variables are the preferences of each individual. The details of the model

are outlined in table 6.

Table 6: Preferences of friends at the cinema, based on the original position

Individual 1stpref. 2nd pref. 3rd pref.

Angela Harry Potter Toy Story Lord of the Rings

Bruno Harry Potter Lord of the Rings Toy Story

Colin Lord of the Rings Toy Story Harry Potter

Doreen Lord of the Rings Toy Story Harry Potter

Ernest Toy Story Harry Potter Lord of the Rings

The contingencies of the example are made clear by analysing the options against both

Condorcet Methods and a Borda Count. While Harry Potter (HP) is preferred to Lord of

the Rings (LR), and LR is preferred to Toy Story (TS), TS is preferred to HP hence

there is a Condorcet paradox across the five voters. Similarly, operating a basic Borda

Count giving a weight of two votes to first preferences and one vote to second

preferences yields a three-way tie with each film receiving five points. Thus, the

situation is wrought with difficulty since two major voting methods fail to yield

conclusive results. Other methods do, however, offer more conclusive results. SMP

declares a tie between HP and LR, thus in effect giving them each a 50% chance of

winning while excluding TS. Meanwhile AV produces a clear result HP is the winner


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after Edwards vote is transferred. A summary of the results yielded by several systems

is outlined in table 7.

Table 7: Candidate victory probabilities under different voting methods

System

Chance of

victory: Harry

Potter

Chance of

victory: Lord

of the Rings

Chance of

victory:

Toy Story

Single Member Plurality 0.5 0.5 0

Instant Runoff Voting27 1 0 0

Coombs Method 0 0.5 0.5

Condorcet Methods 0.33 0.33 0.33

Borda Count 0.33 0.33 0.33

Approval Voting28 31.3 31.3 37.3

That there is considerable ambiguity between different voting systems lends the

example to analysis. If a specific choice of film is yielded by analysis, it follows that all

systems that fail to produce that outcome fail to varying extents at accurately

formalising voter behaviour. Since only Instant Runoff Voting and Approval Voting offer

at least a leaning towards one choice, it is already apparent that several systems are

defective at breaking through the paradox.

Majority Criterion

Given the available preferences, and the knowledge that they are absolute, we can

construct a model to predict the decision-making process by which the friends will

27Includes Alternative Vote, Supplementary Vote and Contingent Vote but excludes Coombs Method in this

specific case for the purpose of analysis, although Coombs is considered an IRV system 28Calculations derived from certain chance of voter approving his/her first choice, 50% chance of approving

his/her second preference and no chance of approving the third choice


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solve their dilemma. The first stage is acknowledging that a problem exists: In this case

there is no majority for any one film and thus the possibility exists that a majority will

actively disapprove of the outcome. This means that there exists a possible circumstance

in which a majority of the friends would choose another option which is absolutely

preferred to the plurality choice. While not inevitable, this mere possibility renders

simple plurality voting insufficient for reflecting the decision-making procedures of

individuals. In any such situation, individuals would perform at least a cursory

examination to insure that the outcome does not yield majority dissent. For a decision

to be made in spite of majority dissent is considered perverse since it violates the

approval criterion set out in section two. This particular example also involves a tie in

that there is no outright plurality winner. However this fact is unproblematic since, as

just stated, the mere lack of majority is sufficient to generate a dilemma. As such, the

first principle of formal legitimacy is thus: It is formally legitimate for a system to require

that the outcome is not subject to majority dissent.

Another way of expressing immunity to majority dissent is to require a system to avoid

electing the Condorcet loser. Majoritarian systems succeed in guaranteeing this since the

winner must defeat a candidate in the final round thus ruling out the possibility that

he or she was less preferred to all other candidates. However, plurality systems such as

SMP and Approval Voting fail to embed this guarantee. Brahms and Fishburns seminal

endorsement of Approval Voting even admits this fact.29 Whilst either system can claim

benefits in other areas, they fail on an important principle of formal legitimacy since it is

simply not plausible that rational voters will settle for a Condorcet loser where it exists.

Therefore, a plurality voting system cannot be formally legitimate.

29Brams and Fishburn: (1983), although the authors challenge the importance of avoiding Condorcet losers in

their analysis anyway


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Prioritising Favourites

First of all, each of the five friends will state their preference for which film to see. So

Angela and Bruno will vote for Harry Potter, Colin and Doreen will vote for Lord of the

Rings, and Ernest will vote for Toy Story. That they purely state their first preference at

the initial juncture is rationally plausible from table 8. Using Angela and Bruno as

examples, if either states only their first preference, the weighting given to that

preference will be one. If either states more than one preference, the weight given to

them will be diminished depending on how many have been stated. The reason for this

is that, assuming each individual adheres to the principle of equity i.e. that each

persons vote ought, in principle, to count equally each persons vote must count for

exactly one at each stage in the contest. Thus expressing more than one preference

diminishes the weight of each preference as a proportion of the single vote available to

each individual. The weighting given to preferences in the table is expressed by the

variable w, and the number of preferences expressed by n.

Table 8: Preference stating dilemma

ROW: Bruno

COLUMN: AngelaState 1stpreference only

State multiple

preferences

State 1stpreference only w1 , w1 w1 , w1/n

State multiplepreferences

w1/n , w1 w1/n , w1/n

Since one of the grounding assumptions of the model is that each friend has an absolute

preference for their favourite film, it follows that each will seek to maximise the chance


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of that film succeeding.30 Hence they will state only one preference each to insure that

the weight of their first preference vote is maximised. This presents the second

principle of formal legitimacy: It is formally legitimate for a system to restrict voters to

stating only their first preference in the first round of voting. As a corollary, it is not

formally legitimate to count more than one preference in the initial round of voting.

Subsequent rounds may or may not exist, but it holds that requiring voters to express a

favoured candidate is formally legitimate.

That this restriction is formally legitimate raises problems for systems that do not

prioritise first preferences. Single Member Plurality systems and most Instant Runoff

Voting methods both place priority in first preferences as only these are active in the

first round of voting. However, Condorcet Extension Methods, the Borda Count and

Approval Voting all violate this priority. The former two systems simultaneously count

all preferences and derive conclusions in a single round of voting. Approval Voting

treats all preferences as equal and counts latent favourites equally with lower

preferences that also receive approval. It is however implausible that any of these

methods would be conducted by rational individuals in the original position. Because

each voter wants to maximise the chance of his or her first choice winning, they will not

rationally compromise that victory probability based on no information about the

preferences of others. We have already seen that prioritarian methods such as SMP and

IRV can yield winners other than the Condorcet or Borda winners: the election in table 9

below is an apt example. In the example SMP hands victory to A, but AV would have

given it to C and a Supplementary or Contingent Vote system would have handed it to B,

despite D being the Condorcet choice and Borda Count winner in all circumstances.

30This is dependent on no friend having information on how the others are voting beforehand, which

would give them reason to seek more tactical ends, and would thus count as a confounding variable


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Approval Voting could have elected any of the four possibilities depending on the cut-off

points chosen by the voters.31 Hence, supporters for A, B and C would have damaged

their chances of a perfect outcome by exposing their second preferences. Tactical

considerations such as avoiding least-favoured outcomes, which may induce different

voting patterns, are void because, in the original position, no voter has information

about the choice of any other voter and thus there is no scope to believe that any voter

would have reason to want anything other than victory for their favoured choice.

Therefore neither the Borda Count, the Condorcet Method nor Approval Voting strictly

reflect the behaviour of voters in the original position, and so go beyond acceptable

levels of formalisation. This leaves only non-plurality, prioritarian systems still standing

after the first two principles have been formed.

Table 9: Example election with ambiguous outcomes


8 voters A D B C

4 voters B D C A

3 voters C D B A

2 voters D C B A

Tactical Voting

At this stage, then, each individual has announced his or her first preference in the hope

that it will succeed, since the ideal circumstance for each voter is to watch his/her first

31

Approval Voting probabilities calculated on the assumption that each voter has a certain chance of listingtheir first preference and a 50% chance of listing their second choice as well, with no chance of listing their last

choice


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choice and that all five friends watch that choice. However, acknowledging the first

principle means that the friends will not settle for the plurality winner based merely on

the first-choices of each voter. In this case, they will not settle to break the tie by

random chance, as would be involved in a plurality contest to determine the winner.

The only way to break the tie is thus to consult more preference data, since this is the

only avenue that retains internal legitimacy.

Various forms of instant runoff voting now advocate forcing the losing voter in this

case Ernest to defect and either choose another option or withdraw his vote from the

contest.32 Given the systemic coercion involved in eliminating a candidate from the

contest, this is an example of the formality involved in IRV. However, in the example we

are assuming that there are no confounding variables such as power dynamics, hence

there can be no coercion as there is no actor or actors to enforce it. Any alterations in

votes must occur voluntarily.

Table 10: Voting dilemma, with publically attainable knowledge in parentheses

Individual Stick with original choice Defect to second choice Utility

Angela 1stor 3rd wins (HP2, LR2, TS1) 2nd or 3rd wins (HP1, LR2, TS2)Stick = 1

Defect = 1

Bruno 1stor 2nd wins (HP2, LR2, TS1) 2nd wins (HP1, LR3, TS1)Stick = 1.5

Defect = 1

Colin 1stor 3rd wins (HP2, LR2, TS1) 1stor 3rd wins (HP2, LR1, TS2) Stick = 1Defect = 1

Doreen 1stor 3rd wins (HP2, LR2, TS1) 1stor 3rd wins (HP2, LR1, TS2)Stick = 1

Defect = 1

Ernest 2nd or 3rd wins (HP2, LR2, TS1) 2nd wins (HP3, LR2)Stick = 0.5

Defect = 1

32In non-compulsory forms of preferential voting, voters can withdraw their votes from the count by stating

no further preferences at a given point, at which point their ballots will be exhausted


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Table 10 presents the dilemmas to each friend as they decide how to cast their second

vote. As stated, the only difference between the votes is that this time each voter has

knowledge of how the others previously voted. If each friend assumes that the others

will stick with their original choices, the expected outcomes are shown by the table in

the cases of sticking and defection. Utility is measured as 2 for a first choice victory, 1

for a second choice and 0 for a third choice victory, although the only relevant

distinction is that the utilities are different and ordered appropriately. In the case of a

tie, the expected utility is the average of the two possibilities. As can be seen, only

Ernest has an incentive to defect. He knows that his first choice is not popular and that,

if a random tiebreaker ensues, he could be faced with his least favourite choice being

decided upon. By defecting, he can at least guarantee that his second choice will be in

the majority and thus protected from defeat by a tiebreaker. Meanwhile, Angela, Bruno,

Colin and Doreen can be reasonably assumed to stick with their choices. Even if they

assume that Ernest will defect, they have no way of knowing which film he favours as a

second preference, thus their expectations do not alter. Since all but Bruno derive equal

utility from sticking and defecting, they have no reason to defect.33. It is therefore

rationally plausible that, given a second vote, Angela, Bruno, Colin and Doreen will

voluntarily choose to stick with their choices while Ernest will choose to defect.

Even if the expected defection of Ernest is added to the analysis, none of the structures

will change. Table 11 shows that considerable ambiguity about the outcome arises

33In Angela, Colin and Doreens case, the lack of incentive either way gives them no reason to defect. Since

defection is an active choice while sticking is passive, the burden of reason falls upon defection, hence they are

more reasonable to stick with their choices if they have no incentive either way. An apt analogy is to consider

the decision to stick as the null hypothesis (h0)and the decision to defect at the alternative hypothesis (h1),thus for a change to be reasonable, the alternative hypothesis must be proven true in order to allow the null

hypothesis to be discounted


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when no one but Ernest knows how he will vote however the expected utilities do not

alter because the information is structurally sufficient.

Table 11: Table 10, Based on expectation that Ernest will defect

Individual Stick with original choice Defect to second choice Utility

Angela 1stor 3rd wins (HP,LR>TS) 1stor 3rd wins (HP,LR>TS)Stick = 1

Defect = 1

Bruno 1stor 2nd wins (HP,LR>TS) 2nd wins (LR>HP)Stick = 1.5

Defect = 1

Colin 1stor 3rd wins (HP,LR>TS) 1stor 3rd wins (HP,LR>TS)Stick = 1

Defect = 1Doreen 1stor 3rd wins (HP,LR>TS) 1stor 3rd wins (HP,LR>TS)

Stick = 1

Defect = 1

Ernest 2nd or 3rd wins (HP2, LR2, TS1) 2nd wins (HP3, LR2)Stick = 0.5

Defect = 1

The principle that is being touted here is that voters for the weakest candidate,

provided with information after an initial round of voting, will voluntarilychoose to

alter their votes if given the opportunity. This voluntary behaviour is analogous to the

formal mechanism of elimination used in the Alternative Vote. By eliminating the

weakest candidate on first preferences, AV reveals an embedded assumption: that the

voters for that candidate would, had they been free to do so over a number of rounds,

have changed their vote according to their second preferences. AV effectively says to the

voter: You cannot have your first choice since it has lost. Your second choice will

therefore be counted in its place. This is justified because, had you been in a free

position and seen the weakness of your choice, you would have voted tactically for your

second preference to ensure, at least, that you dont end up with something less

preferable still. This can be expressed as the third principle of formal legitimacy: It is

formally legitimate for a system, given appropriate preference data, to inactivate the first


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preferences of voters whose candidate has proven the weakest after an initial round of

voting, and activate their second preferences as a representation of how those voters

would vote tactically in such a situation, provided they wished to attain the maximum

returns according to their preferences.

This principle poses problems for SMP and Coombs Method and raises questions about

the Contingent Voting system. SMP, of course, fails to provide appropriate preference

data to allow the second preferences of beaten voters to become active in the contest.

Since this is an acceptable formalisation, SMP falls short of accurately reflecting the

behaviour of voters. Coombs Method is troubled by the requirement that the candidate

strengths must be judged after an initial round of voting. The CM refers directly to the

lowest preferences of voters in determining the weakest candidate, however given the

narrative of the voting procedure in the original position cinema example, no such

preferences have been stated, nor has there been any reason to state such preferences.

The only data that is publically available to influence tactical voting is the favoured

choice of each voter. Hence, the least favourite choice of each voter is opaque in the

original position and, given the first principle that voters will seek to maximise the

chance of their favoured choice winning, there is no situation in which the stating of

least favoured candidates is plausible. Therefore Coombs Method contains a

formalisation that is not plausible, simply owing to the inevitable opacity of least-

favoured choices among rational voters in the original position.

The Contingent Voting System involves the elimination of all but the top two candidates,

regardless of the number of candidates in the race. In the context of the original

position, this is analogous to broadening the definition of the weakest candidate to

encompass all candidates finishing in third place or lower. In essence, the principle


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victory for A remains alive. Since Cs voters, as a logical consequence, have a chance of

victory given this transfer possibility, they will have no reason to defect until Ds voters

have shown where their second preferences lie.34

Hence, the Contingent Vote casts too broad a sweep when eliminating all but the two

strongest candidates. The Alternative Vote is more procedural and more plausible.

Referring back to the example from table 9, a Contingent vote delivers victory for B

while AV delivers victory for C. CV thus prevents Cs voters from realising the potential

victory their candidate has access to, despite the preferential data otherwise favouring a

procedural endorsement of C. Rational voters will therefore conduct decision-making

by procedure since this maximises the opportunity for voters to realise the potential of

their votes. AV is thus the only system that survives all three maxims of formal

legitimacy.

34If the votes for C and D totalled less than the votes for B, provided C and D were third and fourth

respectively and B was secondCs voters would have no further incentive to stick with their choice since they

cannot overtake B based on Ds transfers alone. Some variants on AV are sensitive to this and immediately

eliminate all candidates who cannot overtake the immediate rival above them. This is thus a more efficient andaccurate method for AV to use, although the one-by-one orthodox method of elimination is only mildly

inefficient, and not insufficient a greater problem


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Conclusion

Having explored three distinct areas of legitimacy, it remains to determine which

aspects should be given more weight and thus which counting concepts emerge as the

most important for maintaining maximal legitimacy.

The first section, concerning Internal Legitimacy, pitted plurality concepts against

majoritarian concepts and found that, in this area, simplicity was the main beneficiary.

While complex systems contain more tiebreaking variables, they tend to create

problems of consistency which opens up the possibility of perverse winners35. As such,

plurality systems were concluded best at dealing with issues of internal legitimacy.

The second section: Consent Legitimacy, presented the requirement that a voting system

maximisefreedom through the ballot structure. Restrictive systems such as SMP,

Limited Voting, Block Voting and the Supplementary Vote thus fell short of providing

adequate sensitivity to voters preferences. Permissive systems nevertheless required

non-compulsion in order to deliver authentic preferences and to disambiguate whether

or not winning candidates had met the approval criterion, and so the Australian form of

AV and systems requiring comprehensive preferences for adequate functioning such as

Coombs Method failed in this regard. Hence, permissive and liberal ballot structures

were found to lend most credence to consent legitimacy.

The third section focused on Formal Legitimacy, and found three core principles that

formally legitimate voting systems require: Firstly, that the systems avoid electing

Condorcet losers; secondly, that preferences are examined in stages and not

35By perverse winner is meant, in essence, a beneficiary of the monotonicity violation.


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simultaneously; thirdly that the weakest candidates voters may be reallocated

according to their second preferences. The only voting system that passed through this

analysis unscathed was the Alternative Vote, which accurately embodied the behaviour

of rational voters in the original position. It avoids electing the Condorcet loser,

prioritises the counting of first preferences and eliminates one candidate at a time,

starting with the weakest on first preferences the only publically-observable criterion

for relative strength. Therefore, AV was the specific endorsement of the third section.

Variously endorsing plurality systems, preferential systems and specifically AV in each

of the three areas of legitimacy demonstrates that overall legitimacy cannot be judged

by giving equal weight to each concept. It remains to establish which of the three

concepts Internal, Consent and Formal legitimacy are more important for legitimacy

in the overall sense.

The means by which the concepts themselves can be assessed concerns the nature of

the problems they present. Internal problems areprobabilistic, Consent problems are

contingent, and Formal problems are necessary. Internal problems only blossom in cases

where either stalemates exist or monotonicity produces a perverse winner. The

possibility of either of the problems occurring is small at the very least.36 Consent

problems only exist in the absence of a majority for one choice in these circumstances

there is no reasonable scope to assume that the first preferences of voters are

ambiguous and that any other result can possibly exist after further examination of

preferences. This is the embodiment of the approval criterion, which locates consent

problems in all systems that do not deliver an initial majority and that are not Approval

36Lepelley, Chantreuil and Berg:(1996) for the likelihood of the monotonicity violation


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Voting itself.37 Hence Consent problems are contingenton the existence of a majority or

the use of an approval system. Meanwhile, formal problems are necessaryin that

systems that violate any of the three principles will always violate them in all possible

circumstances. It is the embedded formal assumptions of the systems that are at fault,

and these problems are inescapable. This distinction alone lends most weight to the

concept of Formal legitimacy since it concerns fundamental assumptions that cannot be

avoided. Consent legitimacy is also important, but less so since its problems are

contingent on the ambiguity of the outcome. Internal legitimacys importance is based

entirely on probability and, given the relatively low probability of such problems

arising, is thus not especially important for this assessment.

This essay therefore endorses the Alternative Vote as the most legitimate vote-counting

system. It is the strongest performer against formal requirements and also performs

well on consent requirements. It is however essential that AV have a permissive and not

a constrictive or restrictive ballot structure, and hence the Australian and Papua New

Guinean versions of AV are to be derided. Contrastingly, it performs the worst out of any

system on internal requirements, but these are afforded little weight and thus little

relevance.

As outlined at the outset, this essay is but a chapter of a much larger story. AVs success

is based on an analysis confined to the third stage of the electoral framework as

presented at the beginning. The means by which preferences are formed is an issue of

great concern. The quality of information available to voters and the influence of social

institutions can affect preference formation adversely if information is imperfect or if

37Using Approval Voting itself, there is not approval ambiguity and thus no possible situation in which the

approval criterion can be violated


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institutions are unjust.38 Preference translation is also an important factor in

determining legitimacy. If first or subsequent preferences are insincere it raises

ambiguities about the approval criterion outline in the second section. Combined with

this, if voters simply do not understand how to cast their votes, this further undermines

the basis for deriving express or tacit consent during the counting procedure. Regarding

the fourth stage, the dichotomy between local and global outcomes raises relevant

legitimacy questions during vote aggregation. The debate surrounding proportional

representation is extensive and needs to be acknowledged as a prominent absence from

this discussion. Finally, the way in which decisions are made after an election is a

further area of concern. If a proportional criterion has been adhered to during

aggregation, disproportionate real influence wielded by minor parties during coalition

formation is a problem because real outputs poorly reflect electoral inputs. It is thus

essential to note that, while AV is the most legitimate vote counting system, whether or

not it is the most legitimate electoral system remains to be established.

38Ronald Dworkin (1978) deals with the idea that, if institutions are unjust, preferences cannot be authentic.

This would indeed pose problems for the most fundamental assumptions in voting theory


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University Press

University of Warwick Students Union: Sabbatical Officer Elections 2011, Membership

Solutions Limited, company no. 5525449 (figure 3)

Documents

Dissertation Voting Systems