Instant runoff voting and the Oscars

Did you know that Academy Awards are selected by instant runoff voting?

In a fascinating post, Carl Bialik of the Wall Street Journal describes the nuts and bolts of the Oscar voting process and discusses the relative merits of the current system compared to other proposed voting procedures.

Comments

[Alon Levy]

The article doesn't even mention the main flaw with Instant Runoff, which is that you can make a candidate lose by voting for him.

[Clay Shentrup]

They should just use score voting (aka range voting), which is simpler and hands-down objectively superior. See Bayesian regret figures which prove this here:
http://scorevoting.net/UniqBest.html

Alon Levy: Not being monotonic (the problem you point out) is certainly not the "main flaw" with Instant Runoff Voting. The fact that it ignores exponentially 100% of ballot data, and is severely susceptible to strategic voting, and frequently fails independence of irrelevant alternatives are probably all bigger utility-diminishers.

Here's a look at the horrendous flaws of IRV from a mathematicians perspective:
http://scorevoting.net/IrvPathologySurvey.html

[Lindsay Beyerstein]

Alon: "The article doesn't even mention the main flaw with Instant Runoff, which is that you can make a candidate lose by voting for him."

Yes it does:

But many voting theorists aren't so keen on the system. It's called instant runoff because it is used in political elections in lieu of a two-stage vote in which top candidates compete again if none receives a majority of the vote. Among the potential problems, showing up to vote for your favorite candidate may create a worse outcome than not showing up at all. For example, your vote could change the order in which candidates are eliminated, and the next-in-line candidate on the ballot for the newly eliminated film may be a film you loathe.

[Alon Levy]

Clay, I'm not sure how seriously to take a webpage that says, "You get comparable or more improvement in democracy by switching from plurality to range voting, than you get from the very invention of democracy in the first place." The point of democracy isn't to minimize regret; it's to distribute power well.

[Clay Shentrup]

Alon Levy:

The point of a choice is to maximize utility. An election is a choice by more than one person; so the point of voting is to maximize the sum of all voters' utility (and thus, each individual voter's expected utility).

Power is not the point. Power is just "the ability to change the world". The value of power is just the amount by which one can increase his utility by wielding it. Thus power falls under the umbrella of utility.

The quote you cite is accurate. The increase in utility brought about by switching from plurality voting to score voting is approximately as large as the increase you get by going from non-democratic (random) selection to plurality voting. Thus score voting does indeed cause a comparable improvement to the invention of democracy. This is mathematically/economically sound.

[Roosevelt]

Folks,

The Oscars are nominated by the single transferable vote which does a great job at representing the full range of preferences of Academy members -- they really will have a stake in the outcome because almost everyone will have contributed directly to a nomination. Single transferable vote shares the same ballot with instant runoff voting ,but instant runoff voting is a majority system for one winner.

Then, however, the Oscars use a plurality system for winners -- you vote for one and the one with the most votes wins. That's good for "surprises," although not necessarily for ensuring the choice most representative of the majority wins.

As to Alon's point about instant runoff voting, that sounds "spooky" until you realize that it would never affect how people are running the election. It's a mathematical gripe with no practical meaning.

[Alon Levy]

Roosevelt, it's not a mathematical gripe. Israel was in such a situation in 1999; the prime minister was elected in two round voting. The three viable candidates were right-winger Netanyahu, centrist Mordechai, and left-winger Barak; in a three-candidate situation, two-round voting is equivalent to IRV. In the first round Netanyahu was the clear favorite to win a plurality, with Mordechai and Barak fighting for second place. If Mordechai won second place, he'd easily beat Netanyahu; if Barak did, it was less certain. So a Netanyahu voter's most logical choice would be to vote against Netanyahu in the first round and cast a ballot for Barak instead, in order to give Netanyahu a better chance in the second round.

At the end Mordechai's support slipped and he dropped out, but for about a month the situation seemed to be roughly as I describe it above.

Clay, political scientists will tell you that politics is about allocating power. They're concerned with electoral politics, but a lot less than you are. Within the comparative politics community, the main electoral division is single-member districts versus proportional representation, which has a fairly large impact on how majoritarian the system is. The system used for conducting single-winner elections matters less, since in almost all cases, there will only be two viable candidates regardless of which system is used.

[Clay Shentrup]

Roosevelt:

Your statement that STV "does a great job at representing the full range of preferences of Academy members" is unfortunately subjective and unspecific. While there is no straightforward way to do Bayesian regret calculations for multi-winner voting methods, the fact that STV is so poor in the single-winner case (called "Instant Runoff Voting") suggests that it also does a sub-optimal job in the multi-winner case. Reweighted Range Voting is a simpler and objectively superior multi-winner method that equates to ordinary score voting in the single-winner case: http://scorevoting.net/RRVj.html

As to the issue of being non-monotonic (where increasing support for a candidate can make him lose, and decreasing support can make him win), you aren't appreciating the clear problem here. 14.7 Non-monotonic IRV elections amount to a proof that the wrong candidate has been elected in at least 50% of the mirror image scenarios. For instance, say that candidate X is elected, but would have lost if more people had ranked X higher on their ballots -- then IRV would have picked the wrong winner in that alternate case.

Statistically, about 14.7% of IRV elections are non-monotonic. That means that IRV picks the wrong winner in at least 7.35% of elections. And that's ignoring the severity of the wrongness, and the other problems (like failing independence of irrelevant alternatives) that are even more problematic than non-monotonicity.

I would encourage a little education on this subject by a math and voting methods expert:
http://scorevoting.net/Monotone.html

[Clay Shentrup]

Alon Levy said:

Clay, political scientists will tell you that politics is about allocating power.

You're still missing the point that this falls under the umbrella of utility, which is what voting is about. It helps to think about a non-political election, like the one we held at my company to choose the restaurant for our holiday dinner in December. In the same way that you might say "politics is about allocating power", one of my employees might have said, "picking a restaurant is about getting the best flavor/nutrition/ambiance". Okay, fine. Whatever it is you're voting on, it's just some commodity, be it food, or political power. Your ultimate concern is the value of that commodity. Its utility.

So regardless of whether you are voting on which candidate should have power, or which restaurant to eat at -- your concern as a voter is how satisfied you will be with the election results.

So the measure of voting method performance/quality is...social utility efficiency, which can alternatively be expressed as Bayesian regret.

End of story.

Within the comparative politics community, the main electoral division is single-member districts versus proportional representation, which has a fairly large impact on how majoritarian the system is.

Yes, there is debate about how much satisfaction voters will get with single-member vs. proportional districts. Oh, and a synonym for satisfaction is...utility.

I don't know exactly what you mean about being "majoritarian", considering that majority-winner cycles (where A beats B beats C beats A) are possible. Nor do I see any importance in picking an unambiguous Condorcet winner even when one exists. A rational person only cares about utility efficiency, not about "majoritarianism".

The system used for conducting single-winner elections matters less, since in almost all cases, there will only be two viable candidates regardless of which system is used.

You are dead wrong about this. I linked you to Bayesian regret calculations showing a huge difference in performance between different single-winner voting methods. You fail to understand that the reason that there are only two viable candidates in most single-winner elections is because of the voting method. In almost any voting method that fails the favorite betrayal criterion, you are likely to get two-party domination, and hence only have "two viable choices".

Implementing proportional representation is possibly an improvement, but probably not anywhere nearly as large of an improvement as implementing better single-winner methods, e.g. score voting.

Read:
http://scorevoting.net/PropRep.html

[Alon Levy]

Clay, you're linking to your own not very authoritative website. Practically everyone can write a computer simulation proving that their pet system is the best one. That's why there's peer review and expert consensus - they enable sorting out the good from the bad. Expert consensus could be wrong, but you need to provide some evidence that you're more than a guy with a website.

For the record, majoritarianism means strong rule by the majority, with less concern for minority rights; its antonym is rule by consensus. (I find it strange that you're asking me what it is when your PR page lists Arendt Lijphart's exposition on majoritarianism versus consensualism as a reference). Typically, a majoritarian system will have a single-member-district system for electing the legislature, a two-party system, executive dominance, and a strong centralized government. A consensual one will have proportional representation, a multiparty system, relatively equal executive and legislative branches, and federalism with strong state governments. Britain is a good example of majoritarianism, Switzerland a good example of consensualism. The US is somewhat anomalous in that it is mostly majoritarian when it comes to party makeup, but has a federal government.

[Lazar]

I had always wondered about Oscar voting and the potential for spoilage. At my school, Clark University, we recently conducted a student government election with IRV.

[Clay Shentrup]

Alon:

I would disagree that ScoreVoting.net is not authoritative. It is by far the most authoritative (well-researched and scientifically sound) source for information on voting systems. Warren Smith's simulations and theorems revolutionize the field of election theory, and deprecate most of what has been done prior to the year 2000.

The simulations were published in the William Poundstone book Gaming the Vote, so there has been ample opportunity for criticism. But the source code is freely available here if you'd like to look for any methodological errors:
http://math.temple.edu/~wds/homepage/votetest2.c

This program was not writen with any particular bias, and in fact it used 720 combinations of tunings of 5 fundamental "knobs" (like the ratio of strategic to sincere voters). Warren Smith, the Princeton math Ph.D. who wrote the program, was actually surprised to see that score voting always won (among "non-exotic" voting methods - there are some superior ones that are probably too complex to be feasible for political elections).

You said:

For the record, majoritarianism means strong rule by the majority, with less concern for minority rights;

Obviously. But what's a "majority"? Say you have the following ordered preferences for 3 candidates.

35% X > Y > Z
33% Y > Z > X
32% Z > X > Y

Which candidate does the "majority" want? No matter who you elect, a majority of candidates would prefer to have elected someone else. The point of my rhetorical question "what is majoritarianism?" was that it's effectively a nonsense word that distracts from the real issue of utility.

Typically, a majoritarian system will have a single-member-district system for electing the legislature, a two-party system, executive dominance, and a strong centralized government.

1) There's no such thing as a "majoritarian" system. Any voting method can elect a candidate who is less preferred by a majority of voters to one of the losers. See "Arrow's theorem".

2) The trend of getting two-party duopoly is a result of real (not imaginary) issues, like failure of the Favorite Betrayal Criterion. (I.e. in any system where a voter cannot safely show maximal support for his sincere favorite candidate unless that candidate seems to be viable, the appearance of being viable will outweigh other factors, thus the two major parties will have a veritable monopoly.) The point is, there are specific causes of duopoly, regardless of whether duopoly is correlated with some overarching flavor of government that a human being subjectively labels as "majoritarian".

[Wayne Smith]

The strategic consideration mentioned above applies to at two-round election, but not to IRV/STV. Since there is no second round, you must vote sincerely in the first round. Strategic voting is pretty much eliminated.

[Clay Shentrup]

Wayne Smith:

You are absolutely wrong. There is no deterministic voting method that eliminates strategic voting. Here's a simple example that proves it for IRV specifically:

33% Royal > Bayrou > Sarkozy
15% Bayrou > Royal > Sarkozy
17% Bayrou > Sarkozy > Royal
35% Sarkozy > Bayrou > Royal

Bayrou is eliminated first, then Sarkozy beats Royal 58%-42%.

But the voters in the first row prefer Bayrou over Sarkozy. If they simply "lie" and say that Bayrou is their favorite, then Bayrou wins, and they are rewarded for lying. They get their second preference instead of their third.

All this takes is for them to see the pre-election polls showing Royal has essentially no chance against Sarkozy, but that Bayrou does have a chance. It's fundamentally the same logic employed by some Democratic primary voters, who claimed to prefer Clinton over Obama over McCain, but voted for Obama in the primary because they thought he would have a better chance against McCain.

[Alon Levy]

Clay, if it's authoritative, then which peer-reviewed paper was it published in?

And be careful when you call words "nonsense." They say more about you than about majoritarian government. I may be forgiven for not taking you seriously when you incoherently rant that mainstream comparative politics in nonsense, making criticisms that the literature has already addressed. Lijphart has in fact discussed voting systems briefly, showing that single-member districts always promote majoritarianism: he provides examples from Britain and the US, which use plurality; France, which uses majority; and Australia, which uses IRV. I would add that Russia, which uses (dis)approval, had two main candidates in its Presidential elections back when it was democratic. At one point, he even argues from the experience of the British elections in the 1980s that majoritarianism is sometimes pluralitarian rather than majoritarian.