All of Marcus Ogren's Comments + Replies

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.

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
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2Yair Halberstadt
Thanks - I've rehauled that section. Note a Codorcet method is not sufficient here, as the counter-example I give shows.

Party list methods can be thought of as such, though I suspect that's not what you meant. Aside from party list, I don't recall any voting methods in which voters vote on sets of candidates rather than on individual candidates being discussed. Obviously you could consider all subsets of candidates containing the appropriate number of winners and have voters vote on these subsets using a single-winner voting method, but this approach has numerous issues.

You have to be careful with this argument because it's valid for any candidate-based proportional voting method. All such voting methods rely on the influence of voters who strongly support candidates who get elected being reduced with regard to other candidates, so all of them have such an incentive. (It takes different forms in different voting methods; in STV the incentive isn't to forgo ranking such a candidate altogether, it's to rank such a candidate second or third.) This does not mean the incentive for free-riding is equally strong under all candidate-based proportional voting methods, however, and I do think that strategy is more important under SPAV than under some forms of STV.

This is not a proportional voting method.

First issue: Suppose there are two opposing factions, one comprising 55% of voters and the other 45%, in a three-winner election. The smaller faction fields only one candidate. Let's suppose the 45% of voters marking this candidate as "good" is enough to get her into the top 3. Then this candidate has the most "bad" ratings and is permanently eliminated, leaving the smaller faction without representation. This issue can be addressed by not having the rejected candidate permanently eliminated.

Second issue: Suppose th... (read more)

4Yoav Ravid
I tried to run your second case with six candidates for each faction (A1-A6, and B1-B6), and have 11 ballots that rate all A candidates 'Good' and all B candidates 'Bad', plus 9 ballots that rate all A candidates 'Bad' and all B candidates 'Good'. The results are indeed like you said: And if I make both changes (make rejections non-final and reweigh only based on support for elected candidates) I get: Which is closer to proportionality, but It's hard to know with only 3 seats, so I increased it to 10 and got: Which seems close to proportionality. I also thought that perhaps in the first step of each round the ballots should be reweighed based only on support for elected candidates, in the second step based only on resistance to rejected candidates, and in the third step based on either both or again based only on support for elected candidates. I'll test that next and return with results. Either way, I think a case like this where you have two completely polarized groups is not very realistic in a place where multiple candidate/parties are elected (not a single-winner two-party system), and a voting method like this exists. Even in Israel that is very polarized and doesn't have a system like this you still won't get anything that looks like this ballot arrangement. But It's still good to know what happens in edge cases, so thanks pointing this out :) P.S, I'm putting the data for the candidates and ballots in a reply for anyone who wants to replicate the results.

(Disclosure: Vanessa is my wife.)

I want to share my thoughts on how the LTA can have a large impact. I think the main plan - to understand agency and intelligence fully enough to construct a provably aligned AI (perhaps modulo a few reasonable assumptions about the real world) - is a good plan. It’s how a competent civilization would go about solving the alignment problem, and a non-negligible chunk of the expected impact of the LTA comes from it working about as planned. But there are also plenty of other, less glamorous ways for it to make a big differen... (read more)

Answer by Marcus Ogren110

The two main proposals are sequential proportional approval voting (SPAV) and proportional approval voting (PAV).

SPAV proceeds in rounds. In the first round, the candidate with the most votes wins. In the second round, the ballots are reweighted such that those which have the first winner selected have 1/2 weight and all others retain full weight. This is repeated until each seat is filled, and, in each round, a ballot that has voted for n candidates who have already been elected is weighted at 1/(n + 1).

For an election to fill N seats, PAV looks at e... (read more)

2RyanCarey
Thanks. These algorithms seem like they would be better for passing the independence of clone alternatives criterion.
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