Representativeness Heuristic, Base Rates, and Bayes

23 Apr

From the Introduction of their edited volume:
Tversky and Kahneman used the following experiment for testing ‘representativeness heuristic’ –

Subjects are shown a brief personality description of several individuals, sampled at random from 100 professionals – engineers and lawyers.
Subjects are asked to assess whether the description is of an engineer or a lawyer.
In one condition, subjects are told group = 70 engineers/30 lawyers. Another the reverse = 70 lawyers/30 engineers.

Results –
Both conditions produced same mean probability judgments.

Discussion:
Tversky and Kahneman call this result a ‘sharp violation’ of Bayes Rule.

Counterpoint:
I am not sure the experiment shows any such thing. Mathematical formulation of the objection is simple and boring so an example. Imagine, there are red and black balls in an urn. Subjects are asked if the ball is black or red under two alternate descriptions of the urn composition. When people are completely sure of the color, the urn composition obviously should have no effect. Just because there is one black ball in the urn (out of say a 100), it doesn’t mean that the person will start thinking that the black ball in her hand is actually red. So on and so forth. One wants to apply Bayes by accounting for uncertainty. People are typically more certain (lots of evidence it seems – even in their edited volume) so that automatically discounts urn composition. People may not be violating Bayes Rule. They may just be feeding the formula incorrect data.

Impact of Menu on Choices: Choosing What You Want Or Deciding What You Should Want

24 Sep

In Predictably Irrational, Dan Ariely discusses the clever (ex)-subscription menu of The Economist that purportedly manipulates people to subscribe to a pricier plan. In an experiment based on the menu, Ariely shows that addition of an item to the menu (that very few choose) can cause preference reversal over other items in the menu.

Let’s consider a minor variation of Ariely’s experiment. Assume there are two different menus that look as follows:
1. 400 cal, 500 cal.
2. 400 cal, 500 cal, 800 cal.

Assume that all items cost and taste the same. When given the first menu, say 20% choose the 500 calorie item. When selecting from the second menu, percent of respondents selecting the 500 calorie choice is likely to be significantly greater.

Now, why may that be? One reason may be that people do not have absolute preferences; here for a specific number of calories. And that people make judgments about what is the reasonable number of calories based on the menu. For instance, they decide that they do not want the item with the maximum calorie count. And when presented with a menu with more than two distinct calorie choices, another consideration comes to mind — they do not too little food either. More generally, they may let the options on the menu anchor for them what is ‘too much’ and what is ‘too little.’

If this is true, it can have potentially negative consequences. For instance, McDonald’s has on the menu a Bacon Angus Burger that is about 1360 calories (calories are now being displayed on McDonald’s menus courtesy Richard Thaler). It is possible that people choose higher calorie items when they see this menu option, than when they do not.

More generally, people’s reliance on the menu to discover their own preferences means that marketers can manipulate what is seen as the middle (and hence ‘reasonable’). This also translates to some degree to politics where what is considered the middle (in both social and economic policy) is sometimes exogenously shifted by the elites.

That is but one way a choice on the menu can impact preference order over other choices. Separately, sometimes a choice can prime people about how to judge other choices. For instance, in a paper exploring effect of Nader on preferences over Bush and Kerry, researchers find that “[W]hen Nader is in the choice set all voters’ choices are more sharply aligned with their spatial placements of the candidates.”

This all means, assumptions of IIA need to be rethought. Adverse conclusions about human rationality are best withheld (see Sen).

Further Reading:

1. R. Duncan Luce and Howard Raiffa. Games and Decision. John Wiley and Sons, Inc., 1957.
2. Amartya Sen. Internal consistency of choice. Econometrica, 61(3):495– -521, May 1993.
3. Amartya Sen. Is the idea of purely internal consistency of choice bizarre? In J.E.J. Altham and Ross Harrison, editors, World, Mind, and Ethics. Essays on the ethical philosophy of Bernard Williams. Cambridge University Press, 1995.

Does Children’s Sex Cause Partisanship?

26 May

More women identify themselves as Democrats than as Republicans. The disparity is yet greater among single women. It is possible (perhaps even likely) that this difference in partisan identification is due to (perceived) policy positions of Republicans and Democrats.

Now let’s do a thought experiment: Imagine a couple about to have a kid. Also, assume that the couple doesn’t engage in sex-selection. Two things can happen – the couple can have a son or a daughter. It is possible that having a daughter persuades the parent to change his or her policy preferences towards a direction that is perceived as more congenial to women. It is also possible that having a son has the opposite impact — persuading parents to adopt more male congenial political preferences. Overall, it is possible that gender of the child makes a difference to parents’ policy preferences. With panel data, one can identify both movements. With cross-sectional data, one can only identify the difference between those who had a son, and those who had a daughter.

Let’s test this using cross-sectional data from Jennings and Stoker’s “Study of Political Socialization: Parent-Child Pairs Based on Survey of Youth Panel and Their Offspring, 1997.”

Let’s assume that a couple’s partisan affiliation doesn’t impact the gender of their kid.

The number of kids, however, is determined by personal choice, which in turn may be impacted by ideology, income, etc. For example, it is likely that conservatives have more kids as they are less likely to believe in contraception, etc. This is also supported by the data. (Ideology is a post-treatment variable. This may not matter if the impact of having a daughter is same in magnitude as the impact of having a son, and if there are similar numbers of each across people.)

Hence, one may conceptualize “treatment” as the gender of the kids, conditional on the number of kids.

Understandably, we only study people who have one or more kids.

Conditional on number of kids, the more daughters respondent has, the less likely respondent is to identify herself as a Republican (b = -.342, p < .01) (when dependent variable is curtailed to Republican/Democrat dichotomous variable; the relationship holds—indeed becomes stronger—if the dependent variable is coded as an ordinal trichotomous variable: Republican, Independent, and Democrat, and an ordered multinomial estimated)

Future:

If what we observe is true then we should also see that as party stances evolve, the impact of gender on policy preference of a parent should vary. One should also be able to do this cross-nationally.

Some other findings:

  1. Probability of having a son (limiting to live births in the U.S.) is about .51. This natural rate varies slightly by income. Daughters are more likely to be born among people with lower incomes. However, the effect of income is extremely modest in the U.S. The live birth ratio is marginally rebalanced by the higher child mortality rate among males. As a result, among 0–21, the ratio between men and women is about equal in U.S.

    In the sample, there are significantly more daughters than sons. The female/male ratio is 1.16. This is ‘significantly’ unusual.

  2. If families are less likely to have kids after the birth of a boy, the number of kids will be negatively correlated with proportion sons. Among people with just one kid, the number of sons is indeed greater than number of daughters, though the difference is insignificant. Overall correlation between proportion sons and number of kids is also very low (corr. = -.041).

Nudging

5 May

Nudging the mood?
Important consequential decisions in life are hostage to our mood. What we intend to do (and actually do) often varies by mood. Mood, in turn, can vary due to a variety of exogenous reasons – negative swings can be caused by ill-health (a headache, or allergies) and positive swings can be caused by a nice thing said by someone you meet by accident. This variation is a proof of our irrationality. The irrational aspect is not just misattribution of ill-health to mood, but why mood at all affects our decisions. Being aware of the relationship between mood and decisions can allow one to choose better. Given the central place mood occupies in decision making, it is likely that a nudge to affect the mood would be powerful.

End of a nudge
One of the paper-towel dispensers I use has the following sticker ‘These come from trees.’ This is a famous ‘nudge’ (In Sunstein/Thaler terminology). So far so good. Till perhaps a few months ago, I always read the sticker when I used the dispenser. Yesterday I noticed that I had stopped noticing the sticker. This contrasts with my behavior towards the hotel notes about saving water – which I still read. I think that is so partly because there is so much time in a hotel room. Nudges for quick everyday decisions perhaps need to change over time.

Measuring Partisan Affect Coldly

24 Mar

Outside of the variety of ways of explicitly asking people how they feel about another group — feeling thermometers, like/dislike scales, favorability ratings — explicit measures asked using mechanisms designed to overcome or attenuate social desirability concerns — bogus pipeline, ACASI — and a plethora of implicit measures — affect misattribution, IAT — there exist a few other interesting ways of measuring affect:

  • Games as measures – Jeremy Weinstein uses games like the dictator game to measure (inter-ethnic) affect. One can use prisoner’s dilemma, among other games, to do the same.
  • Systematic bias in responding to factual questions when ignorant about the correct answer. For example, most presidential elections years since 1988, ANES has posed a variety of retrospective evaluative and factual questions including assessments of the state of the economy, whether the inflation/unemployment/crime rose, remained the same, or declined in the past year (or some other time frame). Analyses of these questions have revealed significant ‘partisan bias’, but these questions have yet to be used as a measure of ‘partisan affect’ that is the likely cause of the observed ‘bias’.

French for Bread

14 Feb

Pain is an “unpleasant sensation” in response to actual or perceived injury. It is generally assumed that the purposes of pain are twin—to stop the person from engaging in a behavior that is causing the pain, say continuing to dip hand in boiling water, albeit not water that is being slowly brought to boil, and to “train” (in the Pavlovian sense) the body to not engage in such behavior in the future. Given the purpose, the pain response is poorly implemented in many ways. It also sheds light on how the body is architected.

Think of a system that is coded to send a message to the controller to “alert” it to damage and to ask it to reconsider engaging in activity that is causing the damage (or independently take pre hard-coded action). One envisions that the message is sent in a manner that “makes” the controller pay attention, if such attention is warranted, and efficiently conveys a summary of what is going wrong and to what degree, and what particular action that the user is taking that is causing that to happen. One also imagines an “acknowledge” button that the controller presses to assume the responsibility for further action. Then using this information, controller, depending on the circumstance, takes action, and updates the memory and circuiting, if warranted, to create an appropriate aversion for certain activities.

Such signaling is implemented very differently in our body. Firstly it is implemented as “pain.” Next, pain is not proportional to the extent of the injury. This sometimes creates “irrational” aversion. More bizarrely, some harmful things are pleasant, while some good things are painful. Thirdly, there is no direct way for the brain to acknowledge the signal, assume the responsibility of action, and shut off the pain. Next, and worryingly, depending on the extent to which our brain is distracted (say watching television), pain’s intensity varies (This last point has been exploited to build “treatments” for pain). Lastly, our brains can’t temporarily order the signals shut.

It is ‘possible’ that people may warm up to the science of warming

25 Jan

In science we believe

Belief in science is likely partly based on scientists’ ability to predict.
As M.S. notes, climate scientists accurately predicted that temperatures were going to rise in the future in late 1980s. Hence, for people who are aware of that (like himself), belief in climate science is greater.

Similarly, unpredictability in weather (as opposed to climate), e.g., snowstorms, which are typically widely covered in media, etc., may lower people’s belief in climate science.

Possibility of showers in the afternoon
Over conversations with lay and not to say lay people, I have observed that sometimes people conflate probability and possibility. In particular, they typically over-weight the probability of a possible event and then use that inflated weight to form the judgment. When I ask them to assign a probability to the event they identify as a possibility, they almost always assign very low probabilities, and their opinion comes to better reflect this realization.

Think of it like this: a possibility for people, once raised (by them or others) is very real. Only consciously thinking about the probability of that possibility allows them to get out of funky thinking.

Something else to note. Politicians use ‘possibility’ as a persuasion tool, e.g., ‘there is a possibility of a terror attack’ etc. This is something I have dealt with before but I leave the task of where to people motivated to pursue the topic.

Delay Shooting the Help

25 Dec

Procrastination

Procrastination, delaying without reason doing something that one has to do, makes little sense. If the voluntary delay also causes anxiety, which in most cases it does, it may be particularly pointless. Yet a lot of people procrastinate at least some of the times. Why?

One can make a case for postponing unpleasant things that are avoidable—in fact why bother doing those things at all—but not things that are unavoidable, or things that a person intends to do.

The desirability of a task influences the decision to procrastinate or not. Rationally, it should not matter but the fact that it does provides a possible toehold into why we procrastinate:

  1. Sometimes problems don’t appear to have a good solution right away and one hopes that a solution would appear over time even though one may not have good reasons to think that such good fortune would strike.
  2. For example, one hopes that the ‘unavoidable’ task would become avoidable? Or we wait till the point ‘it is clear’ that the problem cannot be avoided?

Procrastination is understood exclusively as a problem about ordering and assumes that the net amount of time expended on task remains constant, irrespective of order. Perhaps that is a problematic assumption. Starting things later may just mean that we spend less time on the task than we otherwise would. However, one can easily reframe the issue as one about when to spend the reduced time, than one where we must delay achieving the aim of spending less time on the task.

Shooting the help

At times when people are worried, and when well-intentioned people try to help them, they simply become annoyed, or even mildly angry at them. Why is it that we refuse help, or more puzzlingly become angry or annoyed with people who are trying in good faith to be of help.

When people offer advice, they often use munitions from similar events and incidents they have encountered. This can be a bit galling as it undermines the ‘uniqueness’ of our problems. This ‘feeling’ is further compounded by the fact that many a time people are also over-eager and often too quick to offer solutions without a more patient listening to the individuating data. And then arguably many people while eager to help don’t do much thinking (either through incapacity, lack of motivation, or on the assumption that no thought is needed) about the problem itself, and offer comments that are not particularly insightful. And then many a time all people want is a sympathetic ear or a pat on the back. In other words, sometimes public self-pity is all we want. This is typically so when either the solutions are obvious or non-existent.

Outside of this, it is also the case that high achievers are less likely to seek help, and bristle when offered help, for seeking help forces them to face their own vulnerability.

On Love

25 Nov

Mothers spend a great deal of their time and energy on their kids, especially newborns. They spend far more time thinking, and working to ensure welfare of another human being (their kid), than most humans will spend on any other human being, say their romantic partner or sibling. Add to this that till the child reaches adulthood, often till much later, the relationship is overwhelmingly one-way – with children thinking little about their parent’s welfare. Still, most mothers find the experience, and the work that goes with it, greatly rewarding.

Joy despite this sizable disparity has been explained by cynics, but only poorly. While parents proclaim that children bring joy to their lives, it doesn’t cause parents to invest time and money for often similar joy can be had at much lower rates of work. And financial investments, investments of time, the toll on the mother’s body, and inconveniences like lack of sleep, problems traveling, etc. likely outweigh potential financial benefits, which are likely either way away from most parents’ minds.

In this puzzle there are perhaps a couple of lessons about love – one is that relationships that are overwhelmingly one-way, say in resources like time and money, can still be basis for mutual joy; second perhaps is that spending more time on people we love can make those relationships more fulfilling, and us happier.

Measuring Love

Love and to love are vague conceptually and in minds of people who use these terms. The concepts have evolved such that attempts to define or deliberate these concepts rile sensibilities – offend the notion that love is really the domain of emotion, not thought. Such thoughtlessness has meant that nearly everyone can get away with claiming love, even when the overall impact on the quality of life they have on their loved one is a deeply negative one.

One way to think about how much we love each other is to take into account how much time we spend actively thinking about the welfare of those we love. Such exercise when done without deliberation elicits an emotionally biased line up of instances where we were thoughtful. To move beyond such selective counting, for what matters are averages, with a penalty for egregious negatives, one ought to think carefully and honestly, and perhaps base assessments on the testimony of the loved one. Intentionality ought to play a part in calculations but not as a blanket defense – I truly want your welfare but there is nothing in the record that backs up the claim – but to down-weight some instances of sub-optimal decision making under pressure, and limited resources.

Personal Milestone Campaigners

24 May

We have all read about beautiful women undressing to raise awareness about cruelty to animals (less handsome women just don’t care about the animals), men and women strutting on runways wearing fashionable clothes to raise awareness about global warming, intrepid souls sailing across vast oceans to raise awareness about plastic waste in the sea, people climbing mountains to raise awareness about cancer and global warming, and swarms of marathoners running many times a year to raise awareness about breast cancer and of late, St. Jude’s Children Research Hospital. To this pantheon of heroes, add the ‘human polar bear’, who recently swam in a glacial lake in the Himalayas to raise awareness about global warming [BBC].

I often wonder how many things we would have remained in the dark about had it not been for these heroic men and women, and the camera crews in tow. And then I mull over the contributions they have made to the world. It is work by such people and cameras following them that has led 76% of the people to believe that breast cancer is the single most deadly disease afflicting women. (It is the fourth largest.)

Not only do these men and women raise awareness, but they also raise money. The ‘acts’ they perform are now sponsored by corporations; the boosters have their boosters. And all of these incredible personal achievements, which only incidentally flood trophy cases and Facebook walls, have been accumulated selflessly in service of some worthy cause (applause). It also reasons that the money and hours that these selfless volunteers spend on training, recovering from training, registering for races, and organizing events, pales in comparison to the money they raise.