Decision Making with Naive Advice

By ANDREW SCHOTTER*

In many of the decisions we make we rely onthe advice of others who have preceded us. Forexample, before we buy a car, choose a dentist,choose a spouse, find a school for our children,or sign on to a retirement plan, we usually askthe advice of others who have experience withsuch decisions. The same is true when we makemajor financial decisions. Here people easilytake advice from their fellow workers or rela-tives as to how to choose stock, balance a port-folio, or save for a child's education. Althoughsome advice we get is from experts, most of thetime we make our decisions relying only on therather uninformed word-of-mouth advice weget from our friends or neighbors. ! call this"naive advice."

Despite the prevalence of reliance on advice,economic theory has relatively little to sayabout it. In this paper I will survey a set ofexperimental results (see Bogachan Celen etal., 2002; Ananish Chaudhuri et al., 2002;Raghuram Iyengar and Schotter. 2002; Schotterand Bany Sopher. 2002, 2003) that indicate thatword-of-mouth advice is a very powerful forcein shaping the decisions that people make andtends to push those decisions in the direction ofthe predictions of rational theory. More pre-cisely 1 will demonstrate the following:

(i) Laboratory subjects tend to follow the ad-vice of naive advisors (i.e. advisors whoare hardly more expert in the task at handthan they ai'e).

(ii) This advice changes their behavior in thesense that subjects who play games ormake decisions with naive advice play dif-ferently than those who play identicalgames without such advice,

(iii) The decisions made in games played withnaive advice are closer to the predictionsof economic theory than those made with-out it.

* Deparimenl of Economics, New Yoik Llniversity, 269Mercer Street. New York, NY 10003.

(iv) If given a choice between getting advice orthe information upon which that advicewas based, subjects tend to opt for the advice,indicating a kind of underconfidence in theirdecision-making abilities that is counter tothe usual egocentric bias or overconfidenceobserved by psychologists.

(v) The reason why advice increases efficiencyor rationality is that the process of givingor receiving advice forces decision-makersto think about the problem they are facingin a way different from the way they woulddo if no advice were offered.

In all but two of the experiments reported onbelow, subjects engage in what are called "in-tergenerational games." In these games a se-quence of nonoverlapping "generations" ofplayers play a stage game for a finite number ofperiods and are then replaced by other agentswho continue the game in their role for anidentical length of time. Players in generation /are allowed to see the history of the gameplayed by all (or some subset) of the generationswho played it before them and can communi-cate with their successors in generation t + 1and advise them on how they should behave.This advice is in two parts. First, in most of theexperiments discussed below, subjects offertheir successors a strategy to follow. After thisthey are free to write a free-form message giv-ing the reasons why they are suggesting thestrategy. These messages provide a treasuretrove of information about how these subjectsare thinking the problem through, and becausethey have incentives to pass on truthful advice(they are paid half of what their successors eam)I feel confident that this advice is in earnest.Hence, when a generation-/ player makes amove, she has both history and advice at herdisposal.

Actually my colleagues and I investigatethree experimental treatments: In one we callthe "baseline,"' when generation / replaces gen-eration r — i, players are allowed to see thehistory of play of all previous generations and

196

VOL 93 NO. 2 EXPERIMENTAL ECONOMICS 197

receive advice from their predecessors. Thisadvice is almost always private between a gen-eration i — 1 player and his progeny. In asecond treatment, called the "history-only"treatment, subjects can see the entire history butreceive no advice from their predecessors. Fi-nally, in our third treatment, called the "advice-only" treatment, subjects can receive advice butcan only view the play of their immediate pre-decessor's generation. In addition, players careabout the succeeding generation in the sensethat each generation's payoff is a function notonly of the payoffs achieved during their gen-eration but also of the payoffs achieved by theirsuccessors in the game after they retire. Bycomparing the play of f̂ ubjects in these threetreatments we can measure the impact of adviceon behavior.

I. The Impact of Advice in Ultimatum Games(Schotter and Sopher, 2002)

Consider an Ultimatum Game with a $10endowment played a.s an intergenerational gamewhere each generation plays once and only oncebefore it is retired. In our experiments we had81, 79, and 66 generations play this game underthe three treatments descritwd above, respectively.

Since this game is played intergenerationallywith each generation playing once and onlyonce, when a Proposer amves in the lab he orshe will see on the computer screen an amountadvised to be sent. A Receiver will receiveadvice advising the minimum offer he or sheshould accept. Economic theory predicts thatonly a small amount, say, $0.01 will be sent.

A. V^as Proposer Advice Followed?

In Figure 1 we have plotted the amountsadvised to be sent as well as the amounts actu-ally sent by each generation in two treatments ofour intergenerational Ultimatum game experi-ment: the baseline treatment where subjects canboth receive advice and see the entire history ofall generations before them and the advice-onlytreatment where subjects can receive advice butonly see the history of their immediate prede-cessors. As can be easily seen, by and largesubjects simply sent the amount they were ad-vised to send. Advice was followed in a verydirect way.

120

30 40 50

Generation

Generation

FiGUKE 1. AMOUNT SKNT AND Aovjct:; (A) BASEI-FNE

TREATMENT; (B) ADVICE-ONLY TREATMENT

B. Was Behavior Changed by Advice?

Advice had a significant impact on behav-ior. For example, while the mean amountoffered in the advice-only experiment overthe last 40 generations was 33.68 it was 43.90in the history-only treatment. Regressing offerson time indicates that only in the advice-onlytreatment does the time variable have a signif-icant (and negative) coefficient. If one wereto look at the histograms of offers generatedby our advice-only and history-only experi-ments, one would see that the impact of ad-vice is to truncate the right tail of the offerdistribution. In fact while only 10 percent ofthe offers in the advice-only treatment wereabove 50, in the history-only treatment 10 per-cent of the observations were above 80. Thevariance of offers is significantly higher in thehistory-only treatment than in the advice-onlytreatment, indicating that history does not seemto supply a sufficient lesson for subjects to

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Row

12

TABLE

player

1—BATTLE OF THE

1

150.0.

500

SF,XES GAME

Column player

0.30.

0150

guide their behavior in a smooth and consistentmanner.

C. Rejection Behavior

Rejection behavior is also affected by advice.In Schotter and Sopher (2002) we estimate alogit model estimating the probability of accep-tance as a function of the amount sent:

Pr(jc accepted) = +

where x is the amount offered and the left-handvariable is a {0, I} variable taking a value of 1if jc is accepted and 0 otherwise. The results ofthis model estimation clearly indicate that theprobability of accepting low offers (offers be-low 25) is significantly higher in the history-only treatment than in either the baseline ofadvice-only treatment. For example, while theprobability that an offer of 10 is accepted isabout 0.10 in the advice-only treatment, thatprobability increases to about 0.19 and 0.53 in thebaseline and history-only treatments, respectively.

II. The Impact of Advice in CoordinationGames: (Schotter and Sopher 2003)

Consider the Battle of the Sexes game shownin Table 1 when played in the lab as an inter-generational game.

A. Was Advice Followed?

In tbe baseline treatment of our Battle of theSexes game, advice appears to be followedquite often, but the degree to which it is fol-lowed varies depending on the state last period.On average, for the row players it is followed68.75 percent of the time, while for the columnplayer it is followed 70 percent of the time.

In these experiments we measured the beliefsof each generation concerning their expecta-

tions of what strategies they expect their oppo-nent to choose. We did this using a properscoring rule, and this enabled us to define whata subject's best response was to those beliefs.Since in some instances the advice offered asubject was counter to their best-response ac-tion, we can measure the relative strength ofadvice by comparing how often the subjectschose one over the other. When advice and bestresponses differ, subjects are about as likely tofollow the dictates of their best responses as tofollow the advice they are given.

B. Was Behavior Changed by Advice?

One puzzle that arises from our Battle of theSexes experiments is the following. While inthe baseline we observe equilibrium outcomes58 percent of the time (47 out of 81 genera-tions), when we eliminate advice, as we do inhistory-only treatment, we only observe coordi-nation in 29 percent of the time (19 out of 66generations). When we allow advice but removehistory, the advice-only treatment, coordinationis restored and occurs 4̂ 9 percent of the time (39out of 81 generations).

These results raise what we call the "advicepuzzle" which is composed of two parts. Part 1is the question of why subjects would follow theadvice of someone whose information set con-tains virtually the same information as theirs. Infact, as stated above, the only difference betweenthe information sets of successive generations inour baseline experiment is the advice that prede-cessors received from their predecessors,

Part 2 of the advice puzzle is that, despite thefact that advice is private and not common-knowledge cheap talk, as in Russell Cooper etal. (1989), it appears to aid coordination in thesense that the frequency of equilibrium occur-rences in our baseline (58 percent) and advice-only treatment (49 percent), where advice waspresent, is far greater than observed in thehistory-only treatment (29 percent), where noadvice was present. While it is known that one-way communication in the form of cheap talkcan increase coordination in Battle of the Sexesgames (see Cooper et al., 1989), and that two-way cheap talk can help in other games, (seeCooper et al.. 1992), how private communica-tion of the type seen in our experiment works isan unsolved puzzle for us.

VOL 93 NO. 2 EXPERIMENTAL ECONOMICS 199

Finally, note that the desire of subjects tofollow advice has some of the characteristics ofan information cascade, since in many cases asubject is not relying on his or her own beliefs,which are based on the information contained inthe history of the game, but is instead followingthe advice of a predecessor, who is just about asmuch a neophyte as is the present subject.

III. Would People Rathei- Have Advice or Data?(Celen et nl, 2002)

If you had to make a decision would yourather be given some information concerningthat decision or would you rather get advicefrom someone who has seen it. One would thinktbat what you decide will depend on your esti-mate of your abilities as a decision-maker com-pared to those of the advice-giver as well as theinformativeness of the data you might expect toprocess yourself.

To get at this question, Celen et al. (2002)investigated a social-learning experiment with adesign that differed slightly from the intergen-erational game experiments described above. Inthis experiment, eight subjects were broughtinto a lab and took turns making decisions se-quentially in a random order. A round started byhaving the computer randomly select eightnumbers from the set of real numbers | - IO ,10]. The numbers selected in each round wereindependent of each other and of the numbersselected in any of the other rounds. Each subjectwas informed only of the number coiTespondingto her turn to move. The value of this numberwas her private signal. In practice, subjects ob-served their signals up to two decimal points.

The task of subjects in the experiment was tochoose one of two decisions labeled A and B.Decision A was the coirect decision to make ifthe sum of the eight private signals was posi-tive, while B was correct if the sum of theprivate signals was negative. A correct decisionearned $2. while an incorrect one earned $0.This problem was repeated 15 times, with eachof the eight decision-makers receiving a newand random place in the line of decision-makersin each round.

Celen et al. (2002) used three treatments thatdiffered in the information they allowed sub-jects to have. In one treatment (the action-onlytreatment), subjects could see the decision made

TABLE 2-—AGREEMENT AND CONTRARINESS INACTION-ONLY AND ADVICE-ONLY EXPERIMBNT.S

Percentage of actions

Subject type Concurring Neutral Contrary

Sees actionReceives advice

44.274.1

16,69.1

39.216.8

by their predecessor in the line of decision-makers (so the fifth decision maker could seethe decision of the fourth etc.) but no others andcould not receive any advice from their prede-cessors. In another treatment (the advice-onlytreatment), subjects (except for the first one)could receive advice from their immediate pre-decessors telling them to either choose A or B,while in the final treatment (the advice-plus-action treatment), subjects could see both thedecision their predecessor made and receiveadvice from him or her. Subject payoffs wereequal to the sum of their payoffs over the 15rounds in the experiment plus the sum of whattheir successors earned so each subject had anincentive to leave good advice.

The final feature of the experimental design,and the one that distinguishes it from othersocial-learning experiments, was that subjectsdid not directly choose a decision A or B, butrather set a cutoff level between —10 and 10.Once this cutoff was typed into the computer, ittook action A for the dec is ion-maker if hersignal was above the cutoff specified and actionB if it was not.

This design can help us answer the questionstated above; would people prefer to have ad-vice or information. For example Table 2 com-pares the actions of subjects who can only seethe actions chosen by their immediate predeces-sor to those who cannot see what they havedone but can receive an advised action. 1 havebroken down the actions of subjects into thoseactions which agree with the action or advice ofthe predecessor (concurring decisions), thosewhich disagree (contrary decisions), and thosewhich neither agree or disagree with the actionsor advice of one's predecessor (such actions arepossible in this experiment since the subject canalways set a zero cutoff which allows him tochoose A or B with equal probability). By"agree" I mean that the subjects sets a negative

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cutoff when he is told or observes the A actionand sets a positive cutoff when he is told orobserves the B action.

As can be seen, subjects take actions thatagree with the advice they receive 74.1 percentof the time yet copy the actions of their prede-cessors only 44.2 percent of the time. Actionsdisagree with advice only 16.8 percent of thetime as compared with 39.2 percent for theexperiment where only actions could be seen. Inaddition, behavior in the advice-only treatmentwas more efficient in the sense that subjectsmade more correct decisions and hence eamedmore money when advice was available. Whileeamings in the action-only experiment averaged$18.8, they averaged $21.8 in the advice-onlyexperiments. These differences are significant atthe 5-percent level using a Wilcoxon test. Fi-nally, one of the main reasons why advice in-creases the payoffs and hence the welfare of oursubjects is that it has a dramatic impact on thesubjects* inclination to herd (make the samedecision as their predecessor). While in ouraction-only experiments we observed herdingof at least five subjects in a row in only 8 of the75 rounds (10.7 percent), in the advice-onlysessions herding occurred in 25 (33.3 percent)of the rounds. Finally, it is remarkable to notethat in all experiments with advice all herdstumed out to be on the correct decision.

In summary, it appeals that, in thi.s informa-tional setting, words speak louder than actions,in the sense that subjects are more likely tofollow the advice of their predecessors to takespecific actions than they are to copy theirbehavior.

IV. Why Follow Advice?(Iyengar and Schotter, 2002)

The results above lead to the question of whyadvice should be so beneficial. Why shouldpeople give better advice to their successorsthan they gave to themselves? An experimentrun by Iyengar and Schotter (2002) attempts toanswer this question.

In this experiment subjects had to choose anumber,, e, between 0 and 100 called their de-cision number. They were told that they wereplaying against a computerized partner whowould always choose the number 37. After thisnumber is chosen, a random number is indepen-

dently generated from a uniform distributionover the interval [~a, +a] for both the subjectand his computerized opponent. These numbers(the decision number and the random number)are then added together and a "total number" isdefined for each the real and computerized play-ers. Payoffs are determined by comparing thetotal numbers of the real and computerized sub-jects and awarding the real player a fixed payoffof M if his or her total is larger than that of thecomputerized opponent. If his or her total num-ber is smaller, then he or she receives a payoffof m. m < M. The cost of the decision numberchosen is given by a convex function c(e) =e~lt\ where r is a constant. This amount is thensubtracted from these fixed payments to deter-mine a subject's final payoff. By letting /• =500, a = 40, M = 29, and ni - 17.2, andholding the computerized player's choice fixedat 37, our subjects face a rather simple decisionproblem with a quadratic payoff function whosepeak is at 37.

This task was used by Antonio Merlo andSchotter (1999. 2003) to test the impact of in-formation on learning. We used a "surprisequiz" method to test how well subjects learnedthe task put in front of them. In these experi-ments subjects performed the exact task as de-scribed above 75 times and received payoffseach period. When the 75 rounds were over theywere surprised and told that they would play thegame once more, but this time the stakes weremultiplied by 75 so that they could eam for thisone trial an amount equal to the sum of whatthey learned in all of the previous 75 rounds.Their choice in this high-stakes round should bea sufficient statistic for all that they have earnedin the previous 75 rounds since the only waythey can maximize their eamings in this roundis by choosing that decision number that theyfeel is best.

In Iyengar and Schotter (2002) this exactexperiment is repeated but in a slightly differentmanner. Instead of having one subject do theexperiment alone, we sat another "advisor" sub-ject next to him or her at the computer. Theadvisor makes written suggestions to the subjectdoing the experiment as to what he or she thinksis the best choice for that round. The chooser isfree to follow this advice or not, but in onetreatment the chooser is penalized for not doingso with a quadratic penalty function based on

VOL 93 NO. 2 EXPERIMENTAL ECONOMICS 201

the difference between the action chosen andthe action advised. In another treatment, nopenalty is assessed for not following advice; it issimply cheap talk. The advisor's payoff is equalto three-quarters of that of his advisee. After theinitial 75-round experiment run in this manner,both the adviser and advisee are separated andgiven surprise quizzes.

Miraculously, it appears as if the process ofgiving advice and receiving it greatly enhancesthe decision-making abilities of the Iyengaand Schotter subjects. For example, while thesurprise-quiz choices of subjects in the no-advice treatment of Merlo and Schotter (1999)was 51.33, it was 36.1 for advisees and 33.5 foradvisers in the Iyengar and Schotter (2002) ex-periment. The optimal decision number was 37.In other words, the process of giving adviceseemed to focus the attention of advisers on theproblem at hand in a manner that leads togreater learning on their part. Subjects seem toleam better when they give advice and whenthey receive it. We think this is true becausegiving and accepting advice causes a decision-maker not only to think through the problemanother time, but to do so in a manner differentfrom when making decisions alone.

This result offers a possible explanation ofwhy it is advantageous to follow advice when itis offered and why advice is better than actions.The reason is that subjects leam better whenthey give advice, and that advice is thereforeworth listening to. Further, a person receivingadvice must contemplate whether or not to fol-low it, and this process may also foster learning.The process of advice-giving makes us thinkabout the problems facing us differently than wetend to do when we are actually engaged inthem.

V. Conclusion

This paper surveyed a set of papers all ofwhich concentrate on the impact of naive adviceon decisions-making. We have found that ad-vice tends to be followed, changes behavior,and is welfare-improving. We have also ex-plained that the process of giving and receiving

advice fosters leaming. Thus, in some sense,, itis not surprising that subjects behave in a morerational manner when they make decisions un-der the influence of advice.

REFERENCES

Celen, Bogachan; Kariv, Shachar and Schotter,Andrew. "The Advice Puzzle: An Experimen-tal Study of Social Leaming Where WordsSpeak Louder than Actions." Mimeo, NewYork University, 2002.

Chaudhuri, Ananish; Schotter, Andrew and So-pher, Barry. 'Talking Oui"selves to Efficiency:Coordination in Inter-generational MinimumGames with Private, Almost Common, andCommon Knowledge of Advice." Mimeo,New York University, 2002.

Cooper, Russell; Dejong, Douglas V.; Forsythe,Rohert and Ross, Thomas W. "Communica-tion in the Battle of the Sexes Game: SomeExperimental Results." Rand Journal ofEconomics, Winter 1989. 20(4), pp. 568 -87.

"Communication in CoordinationGames." Quarferlv Journal of Economics.May 1992, 107(2). pp. 738-71'.

Iyengar, Raghuram and Schotter, Andrew."Leaming with a Meddlesome Boss: An Ex-periment in Sloppy Principal-Agent Rela-tionships." Mimeo, New York University,2002.

Merlo, Antonio and Schotter, Andrew. A Surprise-Quiz View of Leaming in Economic Exper-iments." Games and Economic Behavior,July 1999,28(1). pp. 25-54.

"Learning By Not Doing: An Experi-mental Investigation of Observational Leam-ing." Games and Economic Behavior,January 2003, 42(1). pp. 116-36.

Schotter, Andrew and Sopher, Barry. "Adviceand Behavior in Intergenerational UltimatumGames: An Experimental Approach." Mimeo,New York University. 2002,

. "Social Leaming and CoordinationConventions in Inter-generational Games: AnExperimental Study." Journal of PoUlicalEconomy, 2003 (forthcoming).