An undead lesson in prospect theory

Posted By Daniel W. Drezner Monday, July 19, 2010 - 1:57 AM Share

So, an explanation for that quick zombie survey:

The two questions were designed to test whether people have consistent attitudes about risk. Risk-averse decision-makers prefer the safe option over a lottery with more risk, even if the expected value of the lottery is somewhat higher. Risk-neutral decision-makers are indifferent between a sure bet and a lottery whose expected value is equivalent to that safe bet. Risk-loving decision-makers prefer the risky option, even if the expected value of the safe bet is higher. Risk averse decision-makers aren't necessarily better or worse than risk-neutral or risk-loving decision-makers, but most political scientists assume that individual attitudes about risk are consistent from choice to choice.

The funny thing is, however, that many people aren't consistent from choice to choice. Prospect theory observes that people will be risk-averse when they believe that they are gaining relative to the status quo, and risk-loving when they believe that they are losing relative to the status quo. This means that the exact same choice can lead to different preferences when framed as a gain or a loss.

For a concrete example, consider my two survey questions. One question:

You are in a fight for your life with zombies. You have acquired enough resources to launch an attack on the living dead. You can launch this attack in one of two ways. Which strategy do you prefer?

A. An attack that leads to the certain destruction of 500 zombies;

B. An attack that has a 50 percent chance of destroying 1000 zombies and a 50 percent chance of destroying only 100 zombies.

1,238 people responded to this survey question, and 61.3% preferred option A -- even though the expected value of option B was (.5*100 + .5*1000 =) 550 zombies killed. When operating in a world of gains, a majority preferred the risk-averse option.

All well and good, but consider the other question in the survey:

You are in a fight for your life with zombies. Your resources are dwindling, and you must choose between some unattractive escape options. Which option do you prefer?

A. A retreat that leads to a certain increase of 500 zombies

B. A retreat that has a 50 percent chance of creating only 100 new zombies and a 50 percent chance of creating 1000 zombies.

Now, both options are bad ones, but option A is the less bad one: only 500 more zombies versus an expected value of .5*100 + .5*1000 = 550 more zombies created. Nevertheless, 57.5% of the 1238 respondents preferred option B. When operating in a world of losses against the living dead, a healthy majority of the respondents was willing to take a risk they weren't willing to take when they were operating in a world of gains.

Normally, these preferences are revealed through questions about money -- would you prefer a sure gain of $500 vs. a lottery, etc. My survey findings suggests that prospect theory also applies to counter-zombie policies as well. And yes, the findings are going into the book.

Question to readers: which current foreign policies do you think can be explained by a prospect theory perspective?

EXPLORE:ACADEMIA, DECISION-MAKING, FOREIGN POLICY, PROSPECT THEORY, ZOMBIES

(7)

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DARRENG

5:24 AM ET

July 19, 2010

EV of incremental/decremental zombies

As a respondent who chose to maximize expected value in both cases, I admit to hesitating over the choices in the 'world of gains' question due to lack of information.

It isn't clear that the value of one less zombie in both cases is uniform. Consider the obvious case where there are only 500 zombies extant; that makes the choice trivial in favor of the certain kill. Even if you assume from the wording of the question that there are at least 1000 zombies extant, the actual tactical value of killing 100, 500, or 1000 may vary non-linearly due to a number of other variables not given in the question.

Just another gambler trying to contribute to Advanced Bayesian Zombie Studies...

MONKEY CORP

8:54 AM ET

July 19, 2010

assumptions

The way I see it from many hours playing strategy games is that you don't need to take risks when you are in front and dominating. If you are in front you should be risk adverse as all you need to do is consolidate the gains you already have and maintain momentum to eventually win. However, if you are behind and the status quo will eventually see you ground down to a loss, then you need to take some risks to turn the game around or you will lose. The are always large problems with presenting these types of intentionally context-poor survey questions and concluding that those who did not answer the way you think they should have are not correct. The different answers reflect the fact that there are different possible assumptions able to be made with the limited data the question supplies. If you get different answers, the problem is not with the responders logic, it is with the limited way you have asked the question. The problem with research based on stats is the assumptions of researcher and subject are hidden.

BUZZ KILLINGTON

12:09 PM ET

July 19, 2010

explanation

To be fair, when considering the choices, and pretending it's a real life situation, the "expected value" is a meaningless statistic, because it can not actually happen. It's a or b. In both of these choices, no matter what happens, you're still going to have more zombies than you can really handle. So, in both cases, I choose the option which at least gave me a chance to minimize the number of them.

That doesn't seem irrational to me, but I'm open to being persuaded otherwise.

DANIEL W. DREZNER

8:48 PM ET

July 19, 2010

You weren't being irrational

Choosing the riskier option in both cases, which you did, is consistent with rational choice axioms.

What's interesting is that majorities picked the risk-loving case in the domain of losses but the risk-averse option in the domain of gains. That does violate rational choice axioms. .

SJC

8:17 AM ET

July 20, 2010

The crazy worstest case scenario

I also picked the riskier of the two options both times because 1) this is what I have learned from films but also because 2) of the life-and-death nature of the situation.

If it really was down to me, a half-finished bottle of Coke Zero, 6 arrowroots and a chainsaw then yes, I would try the riskier option no matter what. However, when it comes to playing the lottery on a sunny Thursday afternoon while I'm eating ice cream, then I might re-think my choices and play it safer.

Clearly the theory must have some kind of spectrum for the 'urgency' of a situation? ie: 10,000 nukes are headed for America vs which grooming strategy is going to help my Yorkie place better at the Westminster Dog Show.

UBOAT53

8:16 PM ET

July 19, 2010

Details

I would argue that the percentage chance of success (or failure) is also relevant. For example, I was willing to take both risks in hopes of the larger reward not because I did the math (simple though it was), but because a 50% chance is somehow "acceptable" to me. If the chance of success had been more in the area of 20%, even if the numbers were jiggered to make the math the same, I probably would not have taken the risk.

HARTYBOY97

10:12 PM ET

July 19, 2010

One small quibble...

...if I remember correctly, its technically not the status quo that determines whether one is in the domain of gains or losses, its a fixed reference point that may or may not be the status quo. But thats probably a little down in the theoretical weeds for a blog posting. However, I'm sure Tversky and Kahneman would, if possible, smile approvingly at your experiment.

I think the most visible example of this in US foreign policy right now is probably Afghanistan. In 2009, the US certainly saw itself entering the domain of losses and, one might argue, that the surge policy was politically risk-acceptant choice. That policy, which essentially is about building a viable Afghani state, was certainly riskier than the Biden's scaled back counter-terrorism based alternative.

And I think a great place to learn more about prospect theory and foreign policy is a book by one of Dan's colleagues called 'Balancing Risk'.