Why our politicians aren’t Median
Scott asks why, if the Median Voter Theorem is true, American politicians aren’t all middle of the road, and barely distinguishable from each other.
Elegant as this proof may be, it fails to describe the real world. Democrats and Republicans don’t have platforms exactly identical to each other and to the exact most centrist American. Instead, Democrats are often pretty far left, and Republicans pretty far right. What’s going on?
He suggests a number of reasons. And they’re all probably true at the margin. But there’s a much more basic reason why parties aren’t clones of each other: preferences are correlated.
I’m going to give a really simple toy example, and we’re going to see that correlated preferences + first pass the post is enough to blow the Median Voter Theorem out of the water.
Let’s pretend there’s only two issues that matter to the American voter. Immigration, and Abortion. And let’s pretend that these issues are binary—they’re either fully legal, or completely banned[1].
40% of voters want abortion to be banned, and 60% want it to be legal.
60% of voters want immigration to be banned, and 40% want it to be legal.
But opinions on these two issues are not uncorrelated. Almost nobody is against abortion, but loves immigration. Pretty much everyone who wants abortion to be banned wants immigration to be banned, and everyone who want immigration to be legal wants to abortion to be legal.
So voter preferences look like this.
Now, if we wanted to satisfy the most preferences, under reasonable assumptions[2] we should ban immigration.
But if you had 4 candidates, representing each of the 4 possible policy choices, the one who advocated this policy would come in a distant third:
| Candidate | Abortion Policy | Immigration Policy | Voter Support |
| A | Banned | Banned | 40% |
| B | Legal | Legal | 40% |
| C | Legal | Banned | 20% |
| D | Banned | Legal | 0% |
I think this models the real world pretty well. Republicans and Democrats don’t just differ a bit on the details, they represent baskets of policies, each of which the majority of their voters want. A party that chose the most popular option for each policy would be less tempting both to democrats and to republicans than their current party.
Other Related Stuff
That’s the gist of the post over, view this as an appendix.
Ranked Voting
Ranked voting schemes tend to mitigate this issue. e.g.
Let’s assume that when picking a 2nd/3rd choice candidate 50% of voters care about abortion more and 50% care about immigration more. Then we get this:
| Candidate | 1st choice | 2nd choice | 3rd choice | 4th choice |
| A (ban/ban) | 40% | 10% | 10% | 40% |
| B (leg/leg) | 40% | 10% | 10% | 40% |
| C (ab leg/im ban) | 20% | 40% | 40% | 0% |
| D (ab ban/im leg) | 0% | 40% | 40% | 20% |
If we use a simple Borda count to give 1 point to 3rd choice, 2 for second and 3 for 1st we would end up with scores:
| Candidate | Score |
| A (ban/ban) | 150 (40*3 + 10*2 + 10*1) |
| B (leg/leg) | 150 (40*3 + 10*2 + 10*1) |
| C (ab leg/im ban) | 180 (20*3 + 40*2 + 40*1) |
| D (ab ban/im leg) | 120 (40*2 + 40*1) |
However even using a Condorcet method we cannot avoid this problem entirely. Consider 5 voters and 3 policies, with the following preferences:
| Amy | Bart | Carry | David | Emma | |
| Abortion | ✗ | ✓ | ✓ | ✗ | ✗ |
| Bail | ✓ | ✗ | ✓ | ✗ | ✗ |
| Curfew | ✓ | ✓ | ✗ | ✗ | ✗ |
Then a candidate who stood for Abortion, Bail and Curfew would be preferred by a majority of voters to a candidate who stood against all 3, even though a majority of voters are against each individual policy when looked at independently[3].
Median Voter Theorem doesn’t apply to First Pass The Post
The Median Voter Theorem only applies to voting mechanisms where if a candidate would be preferred to everyone else in a head to head match, they would also win in a multi-candidate match. This doesn’t apply to FPTP where two similar candidates can split the vote, letting a less preferred candidate win.
Median Voter Theorem basically never applies
The Median Voter Theorem only applies to single peaked preferences. This means that all possible outcomes can be ordered from most X to least X, and everybody just picks an amount of X they want.
So for example, the Median Voter Theorem would apply if everybody was voting on how many immigrants should be let into the country, since then everybody picks a number, and the further away the number of immigrants is from this number the sadder you are.
But it wouldn’t apply if everybody was picking which countries to let immigrants in from, because everybody would rank them in different orders—some people would say the only people we should let in are Canadians, others might say Japanese or Europeans or whatever.
And it definitely definitely definitely doesn’t apply to Presidential elections where you’re voting on an incredibly broad set of policies, each of which people will have their own complex opinions on.
Median Voter Theorem is kind of trivial
As discussed, the Median Voter only applies when:
a) If a candidate would be preferred to everyone else in a head to head match, they would also win in a multi-candidate match.
b) All possible outcomes can be ordered from most X to least X, and everybody just picks an amount of X they want.
At which point it’s obvious the Median candidate will win, because they are preferred to every other candidate in a head to head match (by definition of Median).
Parliamentary Democracies
The Median Voter Theorem only applies when there is a single winner of the election. But most countries don’t actually have a single winner—they have a parliament, and unless a single party is preferred by a majority of the electorate over all other parties, the country will usually be ruled by a coalition.
Under these circumstances parties have an incentive to cater to a particular group of people. Since they can almost exactly match what the group wants, they are almost guaranteed their votes. Someone who tries to take the middle of the road approach won’t get any votes. If proportional representation is used, you would naively expect there to be as many parties as there are seats, each getting exactly one seat. In practice people vote strategically + vote for the most salient parties, so parties tend to be significantly bigger than this.
- ^
Whilst this obviously isn’t true in real life, in practice the real question tends to be whether to move the current policy a bit more to the left, or a bit more to the right, which ends up as effectively a binary choice for most people, unless you happen to want a position exactly between where it currently is and where it will probably end up if your party wins.
- ^
E.g.
- Those who want to ban abortion don’t feel much more strongly about the issue than those who want to make it legal.
- People’s opinion on about one issue doesn’t depend on what policy is chosen for the other, so if you make abortion legal, nobody will as a result change their mind about immigration. - ^
This is an example of Ostrogorski’s paradox.
The ranked voting method you’re considering here isn’t Ranked Choice Voting (RCV), it’s Borda Count
Borda Count works exactly as you say RCV works: The candidate ranked first gets 3 points, the second-ranked candidate gets two points, etc. This method is highly susceptible to strategic voting (voters can help out their preferred candidate by ranking D second instead of voting honestly) and parties can benefit enormously from running “clone” candidates.
RCV (more precisely known as Instant Runoff Voting) works as follows: Tabulation proceeds in rounds. At the start of tabulation, each ballot counts as a vote for the candidate ranked #1 on it. In each round, if a candidate has more votes than all the other candidates put together, that candidate is elected; otherwise, the candidate with the fewest votes is eliminated and their votes are transferred to the highest remaining choices on their supporters’ ballots (if possible). RCV is vulnerable to the center squeeze, so in your example it will fail to elect a pro-abortion, anti-immigration candidate.
I think what what you’re looking for is a Condorcet method; they are guaranteed to elect a “beat-all” winner if one exists and do not have the extreme strategic issues of Borda Count.
Thanks—I’ve rehauled that section. Note a Codorcet method is not sufficient here, as the counter-example I give shows.
Yes. Your counterexample is an example of the Ostrogorski paradox, and there is good evidence that this accounts for a significant portion of why Democrats and Republicans fare similarly in elections despite the Democratic platform being more popular than the Republican platform on most issues.
Don’t forget the Primary Election factor.
Candidates who appear in general elections are actually a subset of even partisan candidates: they are those candidates which won their primary elections. In primary elections, general-election-”electability” is sometimes a factor for voters, but its seldom the top priority.
Even considering that political desires are, as OP shows, grouped, we would still expect more moderate candidates in a system without primary elections. Rational parties would submit candidates which maximize their party’s turnout while minimizing backlash and enthusiasm from opponents. Primary election voters, though, usually lack this concern.
I don’t understand what you’re saying here, but I want to understand.
Can you explain it like I’m 5?
The hypothetical most popular president (from the perspective of the entire population) would lose in the primaries. Their own party would never nominate them, because they would seem like a sell-out to them.
Imagine the following 3 candidates:
A—strongly against illegal immigrants, and quite racist against the legal ones
B—suggests to stop illegal immigration, but make the legal immigration much easier
C—wants to make immigration easier; refuses to debate illegal immigration because “no one is illegal”
A would win the Republican primaries, C would win Democratic primaries. B would lose both.
For most people, B would be preferable to either A or C. But they won’t get to make that choice. They will have to choose between A and C.
.
Let’s make it more complicated, and split the candidate B into two similar candidates: B-R and B-D. Both B-R and B-D have the same position on immigration, but on different topics, B-R leans slightly Republican, and B-D leans slightly Democrat.
A hypothetical rational Republican might say “let’s nominate B-R for our party, because they are most likely to get elected, and at least they agree with us on many other issues—the 100% chance of B-R winning is preferable to a 50% chance of A and a 50% chance of C”. A hypothetical rational Democrat might similarly prefer a 100% chance of B-D over a 50% chance of A and a 50% chance of C.
(And basically, this is what the median voter theorem suggests: that the election will ultimately be between B-R and B-D, rather than between A and C.)
But in a situation with primaries, B-R will lose to A, and B-D will lose to C.
.
I suspect that to a smaller degree this might be a problem with political parties in general, even if without primaries it is probably much smaller. Individuals need allies to win, and people like B-R and B-D won’t find many enthusiastic allies in their respective parties.
Yup, that sounds about right. In Denmark, which have a proportional representative parliament, there recently was a party that tried to combine (kinda-) libertarianism, including support for a UBI with anti-immigration policies. It fell apart after a few years, since that quadrant of the political phase space did not have enough voters for even a small party.
Also, there are parties who goes for the middle of the road. They just cater to the segment of the population who like to see themselves as moderates.
This model also seems to rely on an assumption that there are more than two viable candidates, or that voters will refuse to vote at all rather than a candidate who supports 1⁄2 of their policy preferences.
If there were only two candidates and all voters chose whoever was closest to their policy preference, both would occupy the 20% block, since the extremes of the party would vote for them anyway.
But if there were three rigid categories and either three candidates, one per category, or voters refused to vote for a candidate not in their preferred category, then the model predicts more extreme candidates win.
I’m torn between the two for American elections, because:
The “correlated preferences” model here feels more true to life, psychologically.
Yet American politics goes from extremely disengaged primaries to a two-candidate FPTP general election, where the median voter theorem and the “correlated preferences” model seem to predict the same thing.
Voter turnout seems like a critically important part of democratic outcomes, and a model that only takes the order of policy preferences into account, rather than the intensity of those preferences, seems too limited.
Politicians often seem startlingly incompetent at inspiring the electorate, and it seems like we should think perhaps in “efficient market hypothesis” terms, where getting a political edge is extremely difficult because if anybody knew how to do it reliably, everybody would do it and the edge would disappear. In that sense, while both models can explain facets of candidate behavior and election outcomes, neither of them really offers a sufficiently detailed picture of elections to explain specific examples of election outcomes in a satisfying way.
Interesting—your 40/20/40 is a great toy example to think about, thanks! And it does show that a simple instant runoff schema for RCV should not necessarily help that much...
“But opinions on these two issues are not uncorrelated. Almost nobody is against abortion, but loves immigration…”
Red flag.
Why? That’s a fact about voting preferences in our toy scenario, not a normative statement about what people should prefer.
What do you mean by red flag? Red flag on the author’s side? If so, I don’t understand your sentiment here.
Partisan issues exist.