# On voting strategy

In a voting system like we have in the US (“plurality voting”), we may apply something called the median voter theorem. The median voter theorem says that in a face-off between two candidates, the candidate closer to the median voter wins. Here we’re assuming a one-dimensional preference scale (e.g. left to right) and that voters choose the candidate who is closest to them on the scale. The winning strategy for each candidate is to move closer to the median until they are nearly indistinguishable, and each has about 50% of the vote.

As a result, you can see many politicians shifting their views over time, carefully tracking the median view. In the US, voters seem to be uncomfortable with this optimal strategy, and thus they demand that politicians put on a show of having believed in their current views all along. And then when politicians visibly contradict their previous views it’s used as a gotcha. This is incredibly tedious.

Of course, it does not really seem like the major candidates follow the median. Trump and Clinton, are, after all, very far apart! In fact, I’m puzzled why US presidential elections don’t hew more closely to the median voter theorem. I imagine this is a subject of study for political scientists, but I only have baseless speculation to offer. And of course I’m ultimately trying to say something about the current election cycle.

The obvious way to poke at the median voter theorem is to poke at its assumptions. First, maybe people’s political views don’t fall along a single dimension. Second, perhaps voters do not choose the candidate closest to themselves (i.e. there’s a charisma factor). Finally, maybe it’s not really a face-off between two candidates. Aha!

Yes, in the US, we have this primary/general system, which biases candidates towards the median of their respective parties, rather than the median of the US as a whole. Furthermore, during the general election, there are often third party candidates, for whom people cast “protest” votes. Even if there are no third parties, people may cast protest votes by abstaining or staying home.

If both candidates went straight towards the median, voters would find them indistinguishable. They wouldn’t get excited enough to vote for them. Thus, candidates want to move away from the median to drum up more voters. Now, if those voters are simply staying home, we might expect that they won’t vote no matter what, so why bother appealing to them? But say that people vote for the Libertarian party, that would be a clear incentive for the mainstream candidates to move closer to the Libertarian platform.

What I’m saying is that protest votes makes some sense from a game theory perspective. Although, I’m not sure the impact is actually positive. It hurts your side’s chances while increasing the payoff should your side win. When there are significant numbers of protest voters on both sides, it leads to a more polarized political system. Is that a good or a bad thing?

Now, my comment on the current election. I voted for Bernie in the primaries, because I am further left than Bernie. I live in California, so by the time I voted it was already clear that Bernie would lose (contrary to what I heard from Bernie supporters, Hillary’s victory in California had been consistently predicted in the polls for months). So all my vote really did was send a message to Hillary that some of her support lies in Bernie’s direction.

However, Hillary’s correct response is not to move towards the politics of Bernie, but to move towards the politics of Bernie’s supporters. And so it becomes significant that Bernie’s supporters appear not to be nearly as liberal as Bernie is. A New York Times article argues based on polls that Hillary would actually need to move right to appeal to Bernie supporters. It’s not that Bernie supporters are to the right of Hillary, but rather that the ones who oppose Hillary are to the right of Hillary.  They’re not protest voters, they’re moderates!  I guess they were only voting for Bernie because of the charisma factor.

I can’t say how disappointed and disgusted I am. Next time I vote for a losing candidate, I’ll pay attention to whether I agree with the political views of the candidate’s supporters rather than just the candidate themself.

1. dianne says

Well, some of them were Trump supporters who were voting for Sanders because they were hoping to maximize the chaos. See the poll of Sanders voters in West Virginia that found a significant number were already committed to voting for Trump in the general. Note, not voting for Trump if Clinton won, but voting for Trump regardless. Clinton will never appeal to them and she will never appeal to the “liberal” Bernie bros who can’t deal with a woman as the candidate. She should ignore them and just run a campaign where she continues to be the only adult in DC and points out how ridiculous Trump is. And moves to the left because that’s what is best for the country.

2. Ketil Tveiten says

The study that NYT arrticle is based on has some serious flaws if you’re trying to measure “how far to the left are Bernie’s supporters”; namely it samples a general slice of the population and lumps Republicans (who y’know, hate Hillary and so say the prefer Bernie) in with everyone else to reach the conclusion that Bernie’s people are to the right of the Hillarites; when correcting for what party they plan to vote for in the general election, the Sanderistas are well left of the Clinton crew.

3. says

@Ketil Tveiten,
Well that’s good to hear.

In speaking to many undergrad friends (who are universally Sanders supporters), I was pretty disappointed at how they didn’t actually seem that liberal, and mostly cited character evidence as their motivations. But it can be hard to tell and it would be better not to interpret the data through the lens of one’s own anecdotes.

4. says

On second glance, WaPo article fails to address the main point, which was not about Bernie supporters in general, but about the “never Hillary” subset of Bernie supporters.

5. Elizabeth Leuw says

From my personal experiences with them, I noticed that the “never Hillary” Bernie supporters that I know seemed to have been significantly to the right of me, and I was wondering if that might be a larger trend. I guess I wasn’t the only one who suspected that. The two other trends about “never HIllary” Bernie supporters that I know personally have been that they tend to also believe in conspiracy theories, and they tend to be so vocally hostile to Hillary supporters that I don’t really feel safe around them (anymore). I would never have expected these people to support Trump in any way—generally, they call themselves progressives/are consistently pretty liberal. So the severe reactions from these friends/acquaintances has been quite surprising (and somewhat terrifying) to me.

Fortunately, they’re very much in the minority among Bernie supporters that I know, so at least there’s that. And I’m sure there’s a significant amount of bias, because I’m only seeing the most vocal anti-Hillary people. Even so, it still has been a really unpleasant revelation about them. /sigh

6. Jake Harban says

What I’m saying is that protest votes makes some sense from a game theory perspective.

It may well, but what makes sense from a game theory perspective rarely makes sense from a real world perspective because game theory trades in simplistic assumptions.

For example:

Here we’re assuming a one-dimensional preference scale (e.g. left to right) and that voters choose the candidate who is closest to them on the scale.

Obviously, there’s more to politics than a one-dimensional preference scale; one can be a liberal on most issues yet lose votes by being a colossal racist or support a return to theocratic feudalism and still believe health care is a fundamental human right.

However, it’s the second assumption that I think is so wonderfully reflective of game theory reductionism.

If everyone voted for the candidate whose policies they’d most prefer, Jill Stein would be a shoe-in for the presidency. In the real world, there are so many complications that this assumption is little more than an idle fantasy.

Second, perhaps voters do not choose the candidate closest to themselves (i.e. there’s a charisma factor).

There’s a lot more than that. People make decisions based on charisma, on tribal identity, and on brand image of course. There are low information voters who decide based on what is essentially noise. There are people who decide based on faulty information or even self-delusion; in 2012, Obama doubtless received many votes from people who genuinely believed he had passed health care reform, and in 2004, Bush doubtless received many votes from people who genuinely believed WMDs had been found in Iraq. And then, of course, there’s people who vote based on half-cocked notions of “strategy.”

In the face of faulty information, how do you even classify someone’s political beliefs? There was a time in my life when I didn’t know what a single-payer health care system was, but once someone explained it, I was all for it. Did I become more liberal the minute I knew that this was a thing which could happen?

When I was in high school, I had a fairly extended debate with an advocate of prison reform. He believed prisons should be deliberately made comfortable for prisoners; that their standard of living should be no different than that of ordinary people. At the time, I strongly opposed this idea because I genuinely believed that non-abusive prisons would increase crime. However, now I know that Norway has prisons much like the ones he envisioned and it their crime rate (and recidivism rate!) is incredibly low. Learning these facts changed my view, but did it make me more liberal?

If I support Donald Trump because I like his plan for free college, free health care, and an open border immigration policy does that make me a conservative? If I learn he actually opposes all those things and switch my (intended) vote without actually changing my underlying views, does that make me more liberal or just less wrong?

If both candidates went straight towards the median, voters would find them indistinguishable.

Another absurd assumption. If two candidates are indistinguishable in politics (in the sense of equally desirable, not in the sense of both being beyond the moral event horizon), it doesn’t mean they’ll be distinguishable in competence. If we traveled to the magical world of game theory where both the Republican and Democratic candidates advocated the same politics as Jill Stein, I would evaluate which one has the most experience in that line of work and who would be best equipped to do the actual job.

However, Hillary’s correct response is not to move towards the politics of Bernie, but to move towards the politics of Bernie’s supporters. And so it becomes significant that Bernie’s supporters appear not to be nearly as liberal as Bernie is. A New York Times article argues based on polls that Hillary would actually need to move right to appeal to Bernie supporters. It’s not that Bernie supporters are to the right of Hillary, but rather that the ones who oppose Hillary are to the right of Hillary. They’re not protest voters, they’re moderates! I guess they were only voting for Bernie because of the charisma factor.

Yes, I’ve read that article. Its conclusion is drawn on the strength of fatally flawed data; it concludes that Sanders supporters tend to be moderate by asking them whether they consider themselves liberals, moderates, or conservatives but makes no effort to ascertain their actual opinions. Most people in the US self-identify as far more conservative than they actually are, and the extent of that variance is not necessarily random; just for starters, it probably depends on how exposed you are to Republican messages denigrating the idea of liberalism (without naming any specific liberal policies, since those are too popular) and how susceptible you are to those messages and it also depends, presumably, on where you consider the center to be which is a function of where you live and who you socialize with.

Failing to control for the confounding variables of self-identity bias makes the resulting data useless and any conclusions drawn on them unsupported.

7. themann1086 says

This isn’t a direct correlation, but the this Vox article showed a revealing chart of Sanders supporters who said they wouldn’t vote for Clinton in a general election matchup with Trump, either choosing Trump, someone else, or not voting at all. It showed the favorable/unfavorable ratings these supporters had of various people:

Hillary Clinton (8/91)
Donald Trump (27/73)
Elizabeth Warren (59/15)
Barack Obama (64/30)
Joe Biden (73/21)

Those are bizarre splits since most of the leftist critiques of Clinton (too hawkish, too close to the financial industry) could be applied just as strongly to Biden! And being more favorable to Trump? Ooph.

8. says

@Jake Harban,

Obviously, there’s more to politics than a one-dimensional preference scale; one can be a liberal on most issues yet lose votes by being a colossal racist or support a return to theocratic feudalism and still believe health care is a fundamental human right.

Preferences aren’t defined by people’s positions on the issues, they’re defined by the decisions they actually make. Someone could be left on the issues, but be further right on the preference scale. That doesn’t really invalidate the idea of a preference scale.

Invalidating a preference scale is even easier than that. You need to find three people, one who prefers A to B, one B to C, and one C to A.

If everyone voted for the candidate whose policies they’d most prefer, Jill Stein would be a shoe-in for the presidency.

I don’t think this is true. While you can rightly be critical of data and models, you’re basically substituting… impressions? However bad data and models may be, I think this is strictly worse.

Most people in the US self-identify as far more conservative than they actually are, and the extent of that variance is not necessarily random; just for starters, it probably depends on how exposed you are to Republican messages denigrating the idea of liberalism

Are you trying to suggest that “never Hillary” Bernie supporters systematically identify as moderate because they’ve heard lots of messages denigrating the idea of liberalism? It seems to me that if they were so down on liberalism, they wouldn’t really be Bernie supporters. I would not believe this without evidence.

9. Jake Harban says

Preferences aren’t defined by people’s positions on the issues, they’re defined by the decisions they actually make. Someone could be left on the issues, but be further right on the preference scale. That doesn’t really invalidate the idea of a preference scale.

Invalidating a preference scale is even easier than that. You need to find three people, one who prefers A to B, one B to C, and one C to A.

Of course, it’d be game theory jargon all the way.

Mind you, it wouldn’t be too hard to find someone who prefers Trump to Clinton. I can go to a certain Pharyngula thread and easily find someone who prefers Clinton to Stein. I can nominate myself as someone who prefers Stein to Trump. So your “preference scale” is invalidated, for whatever that’s worth.

I don’t think this is true. While you can rightly be critical of data and models, you’re basically substituting… impressions?

No, just using the ordinary definition of “preference.”

Are you trying to suggest that “never Hillary” Bernie supporters systematically identify as moderate because they’ve heard lots of messages denigrating the idea of liberalism?

That was one of two reasons for the discrepancy. The other was the relative (and shifting) location of the center. A person from Mississippi may say: “I support single payer, so I’m a liberal” while someone from Ontario may say: “I support single payer, so I’m a centrist.”

It seems to me that if they were so down on liberalism, they wouldn’t really be Bernie supporters.

Is that another game theory simplification?

The idea of supporting an abstract concept in theory while opposing every specific example of it (or vice versa) is hardly unprecedented; given consistent denigration of “liberalism” as an abstract concept, many people who support liberal policies in nearly every instance nonetheless oppose the idea of liberalism in general.

I would not believe this without evidence.

Sorry, not in much position to do research at the moment. Just for starters, try looking at the last election (or was it 2012?) where liberal policies passed by referendum even in highly conservative areas.

10. says

@Jake Harban,

So your “preference scale” is invalidated, for whatever that’s worth.

Great, so now you understood one of the points in the OP?

No, just using the ordinary definition of “preference.”

Great, but you haven’t offered any evidence that the majority “prefers” Jill Stein in any sense.

The idea of supporting an abstract concept in theory while opposing every specific example of it (or vice versa) is hardly unprecedented; given consistent denigration of “liberalism” as an abstract concept, many people who support liberal policies in nearly every instance nonetheless oppose the idea of liberalism in general.

No, you misunderstood the point. You claimed that polls were wrong because Bernie supporters identify further to the right than they really are. But in order for this to account for the results, it needs to be systematically true *only* of Bernie supporters.

You know what, why do I even bother? You don’t have to provide any supporting arguments for your claims, you can just make claims and I can just reject them. Business as usual on the internets.