With one of the closest and most polarized elections coming to an end, it’s important to consider how we got here.  Particularly, why is there so much polarization in the first place? One reason may be due to the politicians.  The tendency of people thinking in terms of “Us vs. Them” is a concept that most politicians likely understand, but are also subject to themselves.  As a result, they can deliberately and unconsciously promote the adoption of a bimodal distribution of stances in a country.  In America it can be seen that political parties, congressmen, and presidential candidates are making deliberate efforts to distance themselves from their opposition as much as possible, often with unproductive if not detrimental effects.  

If you see politicians as the scum of the earth, this likely isn’t surprising.  However, I will argue that from a rational analysis standpoint, this should be surprising.

Hotelling Model Analysis

For those unfamiliar with what the Hotelling Model is, I would highly recommend watching this video.  I was going to explain this concept myself, but this video’s explanation and animation quality is honestly better than anything I could ever do.

For those of you who are already familiar know, and I would guess even many of you who just learned have figured out, there is a very strong parallel between choosing the location of an ice-cream cart on a beach and political candidate positioning.  There’s a clear mapping of candidates’ stances / platforms as the ice-cream carts, the voters as the beach-goers, and the ideological distance from a candidate’s positions to a voter as the distance from a beach-goer to an ice-cream cart.

The Puzzling Reality of Politics

It’s with this framework that we consider how odd it is that it seems currently, not only are the views of people becoming more polarized, but the candidates themselves are more polarized and partisan than before.  Regardless of where you lie on the political spectrum, this is not a good thing as it makes it much harder for people to work together and actually do anything.  Of course, the political game must be played.  After all senators need jobs too.  However, it seems that lately many politicians don’t really see their job as much as passing and enforcing good laws as much as it is from getting re-elected, which oftentimes involves sabotaging their opponents from passing and enforcing good laws.  As a an aside, this sounds like a pretty good job right?  Imagine a job where your only responsibility is preparing for an interview for said job again every few years and the only qualification is messing with your colleagues.

However, under the Hotelling model, this should not be the case.  Assuming politicians want to maximize their chances of being elected or reelected, they should position themselves near the voter center of the the political distribution.  In the case of a uniform voter distribution, this is at the middle.

Perhaps counter-intuitively, even with a bimodal distribution of preferences, the ideal location is still near the middle (more precisely the median voter), even if said has very few people there. 

Consider the distribution above, where we have two prominent bimodal peaks of voters, with a few in the center.  Candidate A has a left-leaning ideology while B has a right-leaning ideology.  As a result, both candidates initially center their stance around their core supporters.  However, suppose that A moves near the middle of both peaks.  A’s core constituents would be less happy with her since her stance is now a lot further from them than before.  However, they would still vote for A since she’d still be a lot closer to them than B.  Simultaneously, she would also pick up all of the voters in the center now, as opposed to splitting them before.  In fact, assuming that the opponent is stubborn and doesn’t adjust his position at all, A’s ideal position is just slightly left to B.  That way, A would capture all of the votes to the left and even split half of B’s core votes.

Of course, B would never allow this to happen.  B also would begin slowly inching his position to the left.  In the end then, like before, the optimal equilibrium location for A and B are to both be near the median voter; which is also is the Nash Equilibrium response from both A and B.  However, as discussed to before, this “rational behavior doesn’t actually happen and we can now figure out why.

Not Cost-Free

Although voting does not cost money, it is not free.  Physically voting means taking the effort and time to register and potentially waiting hours at a booth.  Having at least a somewhat informed vote involves taking even more time and effort researching political candidates and their policies.  Given this effort, what’s the payoff?  Statistically speaking, nothing.  On the margin, your vote will almost certainly not matter.  If you take the effort to convince friends and family to also vote, then maybe you can also claim indirect influence of a few dozen more.  However, even close elections will have a margin of several hundred.  Therefore, economically it makes little sense to vote.  However, in good consciousness, I cannot advocate for you not to vote though.  As an aggregate and in expectation, groups of people do make a difference. For example, maybe the probability of your vote only has a .001% chance of making a difference.  However, that difference could be worth billions to the country if the right candidate is elected.  However, then again, billions of impact amortized over the entire population of a country is just a few dollars.  Therefore, if calculating purely from expectation an individual can decide whether it is worth it (if he calculates value over the entire population) or not (if he only cares about accrued value to himself).   If nothing else though, voting at least pays homage democracy.

Armed with this knowledge, let’s imagine that we are in a situation where our two candidates are both positioned near the median voter with only some slight deviations.  Now imagine a voter that’s near one of the bimodal peaks.  From the perspective of this voter, the two candidates are almost exactly the same.  Sure there may be a slight preference towards one rather than the other, but it’s really big enough for this person to care that much who actually wins.  In other words, the marginal benefit of their preferred candidate winning is almost negligible.  If that’s the case, why even bother undertaking the hassle of voting?

Ironically, while I maintain that having polarized elections and candidates is generally not a good thing, it does have one good effect.  It motivates previously lethargic and indifferent voters to actually vote.

Existence of Primaries

The way in which most federal candidates in the United States are elected is not through a direct one-shot vote, but a series of primaries.  The two major political parties, Democrats and Republicans, first select a candidate from a pool of prospective candidates to represent their party, who will then advance to the general election.  

For primary elections, different rules and formats are used depending on the states.  There are several different types, but they range from closed to open.  A closed primary election only allows individuals who are registered for that political party to vote in the primary election, while a more open primary allows anyone to participate.

In a closed primary election, it’s not hard to see why a more polarized set of candidates can emerge.  Here, a candidate has to first win an election that essentially only encompasses roughly one-half of all voters.  These voters for the most part all lie on one side of the political spectrum.  In order to win this primary, it is no longer optimal for candidates to position themselves near the median national-wide voter, but instead near the median voter of their political party.  Continuing the assumption that each party contains ~50% of voters, this results in candidates centering themselves around the 25/75th percentile voter.  This effect can also be prevalent in more open primary elections since voters from a different political party are much less inclined / informed to vote in their opponent’s primaries, albeit to a smaller effect.

Of course, after a candidate wins their primaries, it would be rationally optimal for her to immediately shift her positions more towards the median general voter.  However, in practice this is not feasible.  Candidates will obviously not be evaluated just on whatever they say their position is currently, but also on their past actions, rhetoric, and reputation.  If anything, a candidate who opportunistically shifts away from a previously held stance will not be appealing.  

As an aside, flip-flopping on policies, is irrationally treated by most voters as a bad thing.  This is, to an extant, reasonable since consistent flip-flopping may be a negative signal on a candidate’s trustability and consistency.  However, a candidate who has a change in heart about policy or has enacted regrettable policy in the past should not be treated with as much contempt as they now.  We live in a dynamic world with hopefully a dynamic democracy.  The state of the world as well as people’s ideas change over times.  Therefore, it is ridiculous and even harmful to expect that politicians’ stances are resolute and unmoving.  After all, in a representative democracy, candidates are supposed to reflect the will of the people.  If the will of the people changes, why should candidates be punished for changing with them?

That’s not to say that candidates don’t try become more appealing to the general population after winning primaries.  After securing a primary nomination, it is in the best interest of the candidates to move, or at the very least appear to move, their stances a little bit closer to the median voter.

Effects and Solutions

We’ve talked about how our current system and political incentives structure can perpetuate a bimodal polarization of politics, but is it bad?  In short, yes it’s bad.  For one, it makes people really really angry and close-minded.  If you’re a candidate competing this might not be a bad thing since angry voters are motivated voters.  However, whether people within a country want to or not, they are stuck with each other despite their beliefs.  In the long run everyone would benefit from working together.  Another related problem is that this system implicitly encourages politicians to pander to their base.  It has been shown that it is much more important to convince your core constituents to vote than to try to convince people who do not already agree with you that your ideas are good.  Instead of elections being fought on good ideas, they are now being fought all emotion and mobilization.  This is a vicious cycle as it just further perpetuates polarization and irreconcilability.  

These problems are exacerbated in by the electoral college.  Under this system, not only are politicians free to ignore the concerns of the part of the population that holds a different ideology, they can now also safely ignore non-swing states period.  This effectively results in the policy of an entire country being determined by either the core progressives or the core conservatives in swing states.  Problems that people face in these states are at least still somewhat relevant to other people in the country too.  However, this disproportionate representation does kind of undermine the whole point of representative democracy.

So what are some potential solutions to this?  Well, I’ll start by prefacing that although there are  a few, I don’t really expect them to be implemented as I am of the view that lawmakers currently are too lazy to change or are even incentivized not to change the status-quo.

An immediate solution is simply to make voting easier, or even better, mandatory.  From the models above we can see that polarization exists because there’s a cost of voting for many people.  As a result, voters who do not belong in the core constituency of a party are not likely to vote since they’re relatively indifferent between the outcomes.  Unfortunately, the rational response of a candidate then is to move further away from these individuals and more towards their core base.  If we reduce the costs of voting, then non-core constituent voters may find it once again worthwhile to cast a vote.  If voting is mandatory, then this cost is even further reduced to a potentially negative amount, it’s more costly to vote than not vote.  These techniques don’t have to be particularly severe and can even be fun.  Australia achieved a 90%+ voting rate among voters with free sausages at polling booths and a fine of less than $80 Australian (~$60 US) dollars.

A similar push can be made for allowing primary elections to become more open.  This does present some risks as crafty members of the opposing party may push through a subpar primary candidate to make their preferred party more likely to win a general election.

Of course, we can also abolish the electoral college, but that’s a conversation for another day.

Lastly, people as a whole can become more open-minded and perhaps sympathetic to people who don’t agree with them.  This though, may be the hardest, as it may go against some of our deepest primal instincts.

Part 2…

In part 2, we will look at the technical aspects of some of the models I made and evaluated.