Nicola Frignani

Giovanni Ponti

LAboratory for Theoretical and EXperimental EconomicsUniversidad de Alicantehttp://merlin.fae.ua.es/latex/

UPV - 13/6/2008

Risk vs Social Preferences under the Veil of Ignorance

Antonio Cabrales Nicola FrignaniRaffaele MiniaciGiovanni Ponti

LAboratory for Theoretical and EXperimental EconomicsUniversidad de Alicantehttp://merlin.fae.ua.es/latex/

Risk vs Social Preferences under the Veil of Ignorance

UPV - 13/6/2008

Social vs Risk Preferences under the VOI

Motivation (1)

Risk vs. Inequality aversion (source: wikipedia.org): 1. The reluctance of a person to accept a bargain with

an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff

2. The preference for fairness and resistance to inequitable outcomes.

Rawls (1971), Harsanyi (1977) and the VOI:

1. “…the welfare of each participant but having no partial bias in favor of any participant…”

Social vs Risk Preferences under the VOI

Motivation (2)

Procedural vs. Allocation Fairness: 1. Bolton et al. (2005): “…Our data indicate that choice behaviour is

sensitive to procedural fairness: the opportunity for a fair procedure has much the same effect on the acceptability of a given allocation as does the opportunity to have a fair outcome, though random fair procedures also add risk components to the situation that may also affect behaviour…”

Is the Veil of Ignorance a Concept bout Risk? l Horish (2007): “…If people have social preferences they could be in favor

of an egalitarian distribution even if they are risk neutral…”

1. Are People Inequality-Averse, or just Risk-Averse? 2. Carlsson et al. (2005): “The main finding in this paper is that (even under

the veil of ignorance) many people appear to have preferences regarding equality per se. We have also found that both relative risk aversion and inequality aversion vary with sex and political preferences. On average, women and left-wing voters have higher parameter values for both relative risk aversion and inequality aversion.”

Social vs Risk Preferences under the VOI

Related Literature

Functional Identification: 1. Of RA and discounting: Harrison (08), Eckel (04)2. Of “unconditional altruism”: Cox et al. (05,07,08)3. Risk and inequality aversion (surveys): Amile & Cowell (07),

Bosmans (03), Carlsson et al. (05)

4. Lotteries as fair mechanisms: Bolton et al. (05), Karni et al. (02, 07, 08)

5. Renewed debate on the VOI: Roemer et al. (05,07)

6. Experiments with the VOI: Horish (07), Levati et al (07)

Social vs Risk Preferences under the VOI

Assume the following hypothetical situation…

T1 Phase1 Player 1 :->

Social vs Risk Preferences under the VOI

…or the following …

T1 Phase 1 Player 2 :-<

Social vs Risk Preferences under the VOI

T1: Control treatment (Cabrales et al., 2007)

ST. 3: Agents choose b

Payoffs

ST. 4: A random draw chooses the Dictator (i.e. STRATEGY METHOD)

ST. 0: 4 payoff pairs b are drawn at random

ST. 2: Player position randomly determined

24 rounds with changing option sets (constant across treatments)

Player position randomly determined and known in advance

Strategy method

Social vs Risk Preferences under the VOI

ST. 3: Dictators choose b

Payoffs

ST. 4: A random draw chooses the Dictator

(i.e. NO STRATEGY METHOD)

ST. 0: 4 payoff pairs b are drawn at random

ST. 2: Player position FIXED

Player position fixed and known in advance

Only Dictators choose (i.e. NO Strategy method)

T2: Fixing player position (Cabrales et al., 2007)

Social vs Risk Preferences under the VOI

Payoffs

ST. 4: A random draw chooses the Dictator

ST. 0: 4 payoff pairs b are drawn at random

ST. 2: Player position randomly determined

ST. 3: Agents choose b

UNDER THE VEIL OF IGNORANCE

Player position randomly determined and not known in advance (VOI)

Strategy method in contract decision T3-1: ex ante p=.5 T3-2: p uniformly distributed in [0,1]

T3-1/2: VOI

Social vs Risk Preferences under the VOI

Payoffs

ST. 0: 4 payoff pairs b are drawn at random

ST. 2: Player position randomly determined

ST. 3: Agents choose b

UNDER THE VEIL OF IGNORANCE

Player position randomly determined and not known in advance (VOI)

NO PAYOFF CONSEQUENCES ON OTHERS

T4-1: ex ante p=.5 T4-2: p uniformly distributed in [0,1]

T4-1/2: Lotteries

Social vs Risk Preferences under the VOI

Payoffs

ST. 0: 4 payoff pairs b are drawn at random

ST. 2: Player position randomly determined

ST. 3: Agents choose b WITH NO INFO ON PL. ASSIGNMENT

Player position randomly determined as in T3-2/T4-2.

No info on the assignment protocol T5-1: Dictator Game T5-2: Lottery

T5-1/2: The “ambiguous” treatments

Social vs Risk Preferences under the VOI

Fehr and Schmidt’s (1999) IAP

ui

i j

1-i

Better off

Guilt

1+i

Worse off

Envy

Social vs Risk Preferences under the VOI

Fehr and Schmidt’s (1999) IAP

=> >>0 => concave indifference curves

2

1

1 = 2

=.5 =.2

Social vs Risk Preferences under the VOI

“F&S type” preferences: some alternatives

IAP: 0≤≤≥≥

ESP: ≤≤≤≤

SSP: ≤≤≤≤

EP: ;

Social vs Risk Preferences under the VOI

T1: estimating FSP (Cabrales et al., 2007)

The majority of subjects falls in the IAP case, followed by SSP and ESP. In many cases, the constraints on absolute values are violated About 10% of our subject pool display both and negative For 20% we cannot reject the null hypothesis of EP.

Social vs Risk Preferences under the VOI

T2: estimating FSP (Cabrales et al., 2007)

Since in T2 subjects always play as Player 1 or Player 2, only one FS either or can only be identified.

Given this design constraint, FS distributional preferences are almost identical across treatments (both at the individual and the aggregate level)

Social vs Risk Preferences under the VOI

RA with many goods: a “conservative” approach”

Laffont (1989) on how to frame RA with many goods:

=> In absence of uncertainty, MRS does not depend on RA

Social vs Risk Preferences under the VOI

Cox & Sadiraj’s (2005) model of “egocentric altruism”

Social vs Risk Preferences under the VOI

Cox & Sadiraj’s (2005) model of “egocentric altruism”

=> Even in absence of uncertainty, IA grows with RA

Social vs Risk Preferences under the VOI

The VOI case

=> Even in presence of uncertainty, IA grows with RA

=> Cox & Sadiraj:

=> R&S with “cautious RA”: analytically unmnageable (so far)

Social vs Risk Preferences under the VOI

Maximum likelihood estimation of SPs and RPs

T1-2:

T3:

T4:

ML MLOGIT:

Social vs Risk Preferences under the VOI

Results I: Estimating FSP (=1)

In all treatments (but TR3-2) subjects exhibit IAPs where guilt predominates over envy.

In TR3-2, EPs prevail. Is this an instance that Harsanyi is right? Since in T3-1 the VOI makes envy and guilt absolutely symmetric, only the sum can

be identified (we fix ). Differences (between sums) across treatments are never significant. Is this an instance that F&S are right?

Social vs Risk Preferences under the VOI

Results II: Estimating FSP + RA

Risk aversion parameters are always significant Social preferences are qualitatively consistent with constrained estimates Lower RA in:1. VOI (vs. Control) treatments2. In lottery treatments

Social vs Risk Preferences under the VOI

Individual estimates (TR=5)

=> and are positively correlated with

=> Previous results are turned upside down

Social vs Risk Preferences under the VOI

Results III: social preferences and ambiguity (prel.)

Social vs Risk Preferences under the VOI

Results III: social preferences and ambiguity (prel.)

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Social vs Risk Preferences under the VOI

Conclusions

Further research:

1. Robustness over functional specifications2. Alternative working definition of RA3. Treating “ambiguity” in a non-standard way4. Removing VNM:

1. Weighting probabilities in a non linear way2. If subjects do not max (expected) profits,

(strategic) ambiguity is present in all treatments

Social vs Risk Preferences under the VOI

The End

LAboratory for Theoretical and EXperimental Economics

Universidad de Alicantehttp://merlin.fae.ua.es/latex/

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