Economists approach political competition with a simple but potent hypothesis called the “median voter theorem.” Anthony Downs, a senior fellow at the Brookings Institution, proposed the idea in his 1957 book, “An Economic Theory of Democracy.” Essentially, the idea is this: Any politician who strays too far from voters at the philosophical center will soon be out of office. In fact, there is a dynamic that pushes politicians to embrace the preferences of the typical or “median” voter, who sits squarely in the middle of public opinion. A significant move to either the left or the right would open the door for a rival to take a more moderate stance, win the next election and change the agenda. Politicians will respond to this dynamic, whether they are power-seeking demagogues or more benevolent types who use elected office to help the world. When it comes to the big issues, voters at the midpoint usually get the policies, if not always the exact outcomes, they want.---Tyler Cowen (2010)

New York Times.

The

median voter theoremstates that "a majority rule voting system will select the outcome most preferred by the median voter".^{[1]}The median voter theorem makes two key assumptions. First, the theorem assumes that voters can place all election alternatives along a one-dimensional political spectrum. It seems plausible that voters could do this if they can clearly place political candidates on a left-to-right continuum, but this is often not the case as each party will have its own policy on each of many different issues. Similarly, in the case of a referendum, the alternatives on offer may cover more than one issue. Second, the theorem assumes that voters' preferences are single-peaked, which means that voters choose the alternative closest to their own view. This assumption predicts that the further away the outcome is from the voter's most preferred outcome, the less likely the voter is to select that alternative. It also assumes that voters always vote, regardless of how far the alternatives are from their own views. The median voter theorem implies that voters have an incentive to vote for their true preferences. Finally, the median voter theorem applies best to a majoritarian election system.---

Wikipedia.

When *Bush v Gore* was decided, I would tell my European friends that while the decision was dubious on legal grounds and, perhaps, unpleasant for some civil liberties it would not make much of a difference. I reasoned, mistakenly that, first, in America, the President is hemmed in by Congress, the Courts, a huge, internally conflicted bureaucracy, and relentless lobbying by special interests; second, I appealed to the median voter theorem which suggests to many (see Cowen above) that centrists policies will be pursued by governments wishing to be re-elected. So, in effect, I was predicting that during the first term President Bush would be little different from the President Gore we would have gotten if Florida's ballot had been better designed.

After that failed prediction, I stopped pontificating on US politics.

The Median voter theorem, a beautiful application of rational choice theory to politics, is often deployed in order to explain why, in a two-party system, both parties pursue nearly indistinguishable policies (see Cowen above). That very same theorem, as articulated and developed by Anthony Downs (see here the classic article), also explains why for *homo economicus* it is rational not to to vote (the benefit to be gained from an individual vote is far outweighed by the dangers on the road to the polling station) or to be very uninformed of political issues (too costly to become informed), unless (this is often not noticed) one is especially passionate about a given issue or one's economic interest is tied to a particular policy.

Problem is, as deployed by Cowen and as stated by *Wikipedia* the Median voter theorem is manifestly false. (I say this not because President Bush falsified my prediction.) For it makes a further assumption (not explicitly specified by *Wikepedia*): that is, the outcome predicted by it *also* requires that the distribution of voter preferences is normally distributed. When voters are not normally distributed there is, *ceteribus paribus*, no reason to expect that voters at the midpoint more or less get what they want (or that politicians will pursue centrist policies). In re-reading Downs' original and truly fascinating article (about which more before long), I noticed that Downs, too, had recognized the point:

Stable government in a two-party democracy requires a distribution of voters roughly approximating a normal curve. When such a distribution exists, the two parties come to resemble each other closely. Thus, when one replaces the other in office, no drastic policy changes occur, and most voters are located relatively close to the incumbent's position no matter which party is in power. But when the electorate is polarized...a change in parties causes a radical alteration in policy. (143)

So, as originally formulated (yes, I have heard of Hotteling and Black) by Downs the Median voter theorem recognizes the significance of underlying distributions.

I have no idea if the underlying distribution of the American electorate is genuinely polarized now. Even if it is clear that in present opinion polls (a) a larger than usual number of Democratic primary voters are pushing the Democrats toward the left, and (b) a majority of Republican primary voters seem to reject the Republican establishment (Trump, Cruz, and Carson jointly have about 60% of the vote), it does not follow that we are witnessing the generation of, say, a more bi-modal distribution. (Primary voters may not represent the majority of the electorate and many Trump voters -- the old so-called 'Reagan Democrats' -- are, in some respects , more *left*-wing than the pre-Trump Republican party, after all.) All I am claiming is that the median voter theorem does not entail that 'the center' will always hold; if voting blocs seriously disagree with each other, one side may well elect politicians that reject centrist policies even in the American system. (I am ignoring some further ambiguities about what the median is a median of.) Of course, there may be reasons to reject a rational choice model of politics (or an overtly simplistic rational choice model), but it is not obvious that in so doing we get a reason to expect centrist outcomes.

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Posted by: enock | 01/16/2017 at 01:21 PM