Their assumption relies on everyone voting honestly.

No, this isn’t about voting. This is about actual preferences.

there are two different strategies that a voter can use (bullet voting and team bullet voting).

Again, this is simply false. An obvious example would be a Green supporter who normally casts a tactical insincere vote for the Democrat. With Score Voting, he’d generally want to give a max score to the Democrat and the Green. This is not bullet voting. Again, here is a link which discusses the optimal Score Voting strategy as a generalized formula.

Why should elections come down to a more or less random result according to how aggressively or defensively people decide to vote?

Election results should come down to what voters want, and should try to maximally uphold the will of the people. According to Bayesian regret calculations, Score Voting does exceptionally well on this fundamental metric.

Defining an arbitrary social utility function isn’t really an argument anyway.

It is not “arbitrary”.

Austrian economists have proposed the idea that preferences can only be meaningfully measured ordinally, which equally applies to any social utility.

That idea has been debunked to high heaven via simple revealed preference experiments using lotteries. This is one of the most elementary and obvious facts in the whole of economics.

In fact if you ignore the very subjective account of “how much” they prefer a given candidate to another, it resolves a lot of really thorny mathematical issues that occur for voting systems like score voting.

Again you have this completely backwards. Ordinal (ranked) methods are plagued by issues like Arrow’s Theorem and failure of independence of irrelevant alternatives, which cardinal (rated) methods escape. You have not cited any “really thorny mathematical issues” related to Score Voting.

They still took the condorcet winner when there was one.

I don’t know what you mean by “they took”. It is easily demonstrated that the Condorcet winner is not always the social utility maximizer, as seen in this table.

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There is no guarantee whatsoever that score voting will pick the condorcet winner. It isn’t a condorcet method and isn’t even guaranteed to pick a majority winner, let alone a condorcet winner.

I just cited a mathematical proof to the contrary, from a Princeton math PhD who is arguably the world’s foremost expert on voting methods. More specifically, if all voters use rational optimal strategy (attempt to game the system to the fullest extent), then they get the Condorcet winner. If they are more honest, then they do even better (because again, the Condorcet winner is not always the best candidate). Also, Condorcet methods often do not elect Condorcet winners, due to tactical voting.

Also the best strategy is still bullet voting, or team bullet voting

Incorrect. Notice how many voters are insincere under the current status quo where they are forced to only vote for one candidate.

There’s nothing useful about comparing your preferred voting system to random ballot. I mean it’d be pretty freaking useless if it wasn’t better than random ballot.

The point is to show that you made a blatant logical fallacy. You were thinking about vulnerability to tactical voting (slope) rather than social utility efficiency (height). If you really want to minimize tactical voting, then you’d pick Random Ballot and just accept getting horrifically unsatisfactory election outcomes. The fact that you don’t proves you actually do understand that the issue is about utility, at least on some level.

if you vote for your favorite party as well as your political allies, then you’ve effectively cast two votes against your political enemies

As I just trivially demonstrated, the power of one’s ballot has nothing to do with how many candidates you support. Score Voting fundamentally gives all voters equal power. This is just a mathematical fact.

At that point you’re no longer expressing meaningful preferences anymore, just an assessment of whether you think your political allies need your vote to keep your enemies from winning or not, the rest coming down to a game of chicken.

I don’t know why you’re talking about strategic voting again. As our Bayesian regret results demonstrate, Score Voting outperforms the other (much more complex and opaque) systems with any ratio of tactical to honest voters.

If you don’t think strategic voting is a problem then maybe you should look up the history of what happened to bucklin voting.

A. I co-founded the Center for Election Science and wrote their page on Bucklin voting, and even went to the San Francisco public library to look at hand-written Bucklin voting results from the early 1900s. There is no evidence that Bucklin voting faced problems with tactical voters. See the account on my page by one Mayo Fesler of the Cleveland Civic League, as well as Warren Smith’s Bayesian regret figures for Bucklin.

B. Score Voting is dramatically different than Bucklin voting, so it is better to study the effects of tactical behavior with Score Voting than with Bucklin voting. Which we have extensively done.

Producing ties more often is not a desirable property.

Of course it isn’t. And Score Voting actually reduces the risk of ties. I wasn’t saying anything about the risk of ties. I was just using a tie scenario to demonstrate that Score Voting satisfies voter equality. I could have used a scenario where X leads Y by 50 points, and Y leads Z by 23 points, and the relative differences are the same after one of us bullet votes for X and the other votes for Y and Z. Do you understand? I was just using a tie because it’s easier to follow.

Neither is reversal symmetry, outside of the most obvious situations.

Of course reversal symmetry is a desirable property. If all individuals have the exact opposite preferences, it is logically necessary that the group also must.

if you’d read any of the other two articles in this series (or this paper), you might have known that minimax+tideman-score has all of the beneficial properties of score voting, plus many that it doesn’t have (like a strong resistance to tactical voting).

As I already said, we don’t care about “strategy resistance”, we care about Bayesian regret. If you didn’t measure this for your system, you have no idea how good it is. And I’ll bet my first born child that it’s more complex and opaque than Score Voting. Further, Tideman’s “strategy resistance” methodology is a nonsense concept that is basically about as good as a coin toss at differentiating the relative quality of two voting methods. Key excerpt:

Tideman’s “strategy resistance” measure is flawed

This is a magic way of assigning any voting method a number from 0 to 10 with greater numbers being “better.” It incorporates statistics from 87 real ranked-ballot elections. Unfortunately I must criticize this as very flawed. It probably is a somewhat better measure of voting-system quality than a random number — but not by much.

My suspicions of this number were first stimulated when I observed that, according to Tideman’s measure, the “strategy resistances” of Plurality, Range, and Approval voting were 6.3, 4.0, and 3.9 respectively (table p.237) where larger numbers are better. These three numbers are ordered exactly oppositely to what I would expect based on, e.g, the fact that Approval was the only voting method in that table explicitly designed to be strategy-resistant (albeit Tideman’s measure, insanely, gives it the worst strategy-resistance score of all the 25 voting methods in table 13.1!)

One reason underlying that is the following. Consider a 9-way plurality election such as the 2000 US Presidential election contested by Gore, Bush, Browne, Nader, Hagelin, Moorehead, Phillips, McReynolds, and Buchanan. In this race, it is known from NES polls that over 90% of the Nader- and Buchanan-favoring voters, actually strategically voted for somebody else (generally, Bush or Gore). So strategic voting was tremendous, as it is in every US presidential election. But Tideman’s measure would not count this as strategic voting at all! Specifically, if different-feeling voters (say Nader>Gore>Bush voters, Moorehead>Gore>Bush voters, and Nader>Gore>Moorehead>Bush voters) adopt a common strategy (voting “Gore”) that is not counted as strategic voting in Tideman’s reckoning. And if the strategy does not affect the election winner, it similarly does not count (even if the voters do it in vast multitudes).

My opinion still stands that all of the hype about range voting (and approval voting, and STAR voting, and instant runoff) are nothing more than propaganda.

I’ve cited ample evidence to the contrary, and by all indications, you don’t understand it.

If a voting system can’t even pass simple tests like majority winner or condorcet winner then it’s pretty much useless, and score voting fails those tests spectacularly.

I cited mathematical proof that the correct social welfare function must fail the majority and Condorcet criteria. I repeat: these are flaws not benefits, and this is mathematically proven, and is one of the most basic facts of social choice theory.

As William Poundstone’s 2008 book Gaming the Vote explains:

So what does the impossibility theorem mean? … The message of the impossibility theorem is: don’t use ranked voting systems. “There is an open door to social choice,” Hillinger says, “and another one … that is closed. One would have expected choice theorists to pass through the open door; they chose instead to bang their heads against the closed one.”

Advocate of Score Voting and Approval Voting. Software engineer. Father. Husband. American.

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