Elections: just as irrational as human behavior in general

A friend of mine sent me a link to an article by Danny Hillis on elections. Danny is a smart guy who has done good work in many areas, but his analysis struck me as a) radically oversimplified and b) wrong in some important ways. But it got me thinking about how our changing understanding of human rationality (or lack thereof) in economics might spill over into political science. Let me start with how human behavior differs from classical economic models and move from there to how elections are effected.

Traditionally, economics was based on the notion of rational actors. Each individual makes decisions to maximize their utility functions (think about  a modern version of quantifying the notion of “greatest good” in Utilitarianism). Person A might value summers off more highly than a chance at millions of dollars and therefore go into teaching. Person B might dream of having their own private jet and be willing to work nights and weekends to keep even a small hope of their dream alive. But all of these are rational decisions based on utility functions which describe how much each economic actor values each benefit.

It seems reasonable (to a quantitative person such as myself) to think that human economic behavior works this way and the mysteries of the different choices people make is encapsulated in this unknown and in all practical respects unknowable utility function. Unfortunately for those of us who like simple mathematical explanations of human behavior, people don’t actually behave this way. In 1953 Maurice Allais wrote a paper (warning: it is mostly in French, 44 pages, and costs $10 to download) describing a paradox which showed that even if you look at simple financial wealth, people do not rationally follow a utility function. His paradox attacked the notion that if some percentage of the time (say 98%) two options produce the same outcome, we should base our choice between the options on the 2% of the time when they produce a different outcome (in economics-geek-speak, this is the Independence axiom in the Von Neumann-Morgenstern utility theorem). It seems rational (and official, now that it is part of a theorem), but in fact we care very much what happens in the 98% – we do not ignore the identical part of the two scenarios in evaluating them, irrational as that may seem.

Detailed example:

In scenario 1a, you receive $1 million 100% of the time. In scenario 1b, you take a 1% risk of losing your $1 million prize to gain a 1% chance of increasing its value to $3 million. 1% chance of nothing, 98% chance of $1 million, 1% chance of $3 million.

In scenario 2a, you have an 2% chance of receiving $1 million, in the other 98% you receive nothing. In scenario 2b, again you take a 1% chance of losing your $1 million prize to gain a 1% chance of increasing its value to $3 million. 1% chance of 3 million, 98% chance of nothing.

Some people (a reasonable number I would guess) would choose 1a over 1b but 2b over 2a. Mathematically speaking, both decisions are identical: you are giving up a 1% chance at $1 million to increase a $1 million prize to $3 million 1% of the time. The other 98% doesn’t matter. But psychologically, it matters a lot. When you are guaranteed $1 million dollars, risking it sounds irresponsible. And if that 1% chance happens, you will live forever with the knowledge that your greed to get $3 million cost you $1 million. In the other situation, if you don’t get anything, you aren’t surprised and you are fairly confident that it had nothing to do with your decision to increase the odds of getting nothing from 98% to 99%.

Now, on to politics.

Hillis lays out a simple left-right political spectrum. He puts two candidates on it and models voting behavior as people voting for whichever candidate is closer to their beliefs. From this, we can deduce all sorts of things, some of which – like elections being close – sometimes model reality pretty well. Then again, Herbert Hoover never participated win or lose in a close presidential election, and how many electoral votes did Walter Mondale get in 1984? 13. Which is 5 more electoral votes than Alf Landon received in 1936!

The problem is that elections are much more complicated than Hillis’s model. Lets put aside for a second that there are multiple issues involved so it is not a simple one-dimensional spectrum. Lets assume there are only two candidates in the election. Lets also put aside candidates personal charm or lack thereof and their potentially scandalous sexual, military, or substance consumption histories. This model is an still an oversimplification in two critical respects:

1. Voters do not have a simple choice between voting for the Democrat and voting for the Republican. They can stay home. Or they can volunteer or donate money or attempt to harangue their friends into voting for the candidate of their choice. Imagine an (exaggerated, to make a point) election where:

a) 60% of the electorate prefers Smith to Jones, but only by the narrowest of margins; they are generally dissatisfied with both candidates

b) 40% of the electorate strongly prefers Jones to Smith – in fact they thing Jones is close to their ideal candidate and Smith is so nightmarish a candidate they would consider leaving the country if he were elected

What happens in that election? Maybe a 48% turnout; 36% of population (90% of the Jones supporters) vote for Jones and 12% of the population (20% of the Smith supporters) vote for Smith. Jones wins in a landslide, with 75% of the vote. Smith, despite a 20 point margin in polls of registered voters, can’t even carry his home state.

Is this exaggerated? Yes, but intensity matters.

2. Just as the 98% that was unchanged effected the outcome in Allais’s paradox, candidates not on the ballot effect voters. Again, here’s a scenario:

The Yellow party and the Purple party each have 50% support. Both of them nominate a candidate who is free of scandal but not particularly personally charming. Each candidate represents the mainstream of their party – put them just slightly to the center of the middle of their party’s 50%, at say the 30th and 70th percentile respectively.

So far, it sounds like a close election.

However, in the Yellow Party primary Mr. Gold had to duke it out with Mr. Canary. Canary was just a few points further from center than Gold, so the primary was very close, and neither party had a majority of committed delegates at the convention. Mr. Gold did have a slight lead over Mr. Canary, so when the super delegates broke strongly for Gold (whom they felt was more electable) they felt they weren’t overturning the will of the people. But the Canary camp felt like if you included the Canary, Maize and Buff delegates (who endorsed Canary when they dropped out, but such endorsements aren’t binding on their delegates so they were counted separately) against the Gold and Ecru delegates (Ecru having thrown his support to Gold), Canary held a lead before the super delegates voted.

The Purple party primary, however, was a different story. Mrs. Plum was the only mainstream candidate; Mrs. Indigo and Mrs. Magenta were really fringe candidates who generated very little support. The party became unified behind Mrs. Plum in February.

How does this election turn out? Not close at all. About half the Yellow party voters are profoundly upset with the Gold campaign and their party. Many of those voters don’t have an ideological problem with Gold per se, but they are so disappointed with how the process played out for Canary (who wasn’t picked as VP) that they are not at all motivated to vote. Despite being weary from the primary, the half of the Yellow party that supported Gold turns out 60% of their voters giving gold 30 million votes, but only 40% of the Canary voters turn out at the general election. Those that do vote reluctantly for Gold, giving him another 20 million votes for a total of 50 million. Meanwhile, 60% of the Purple party voters show up, giving Mrs Plum 60 million votes and a 10 million vote margin.

If that seems farfetched, I can introduce you to some Hilary Clinton supporters who are strongly pro-choice, support gay marriage, and voted for John McCain.

Now, I constructed both of these scenarios while leaving in place many oversimplifications. Overlay multiple issues of varying intensity and varying degrees of organized lobbying with ethnic, religious, and gender identification and elections become very complex things. Certainly the practical modeling of individual factors is quite advanced; I am curious what the intellectual underpinnings are, and to what extent they have embraced the latest thinking in human economic behavior.

— Max

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