[EM] The worst about each system; Approval Preferential Voting (new name for an MCA-like system)

[Dave Ketchum]

On May 25, 2010, at 1:20 PM, Jameson Quinn wrote:

> What are the worst aspects of each major voting system?

Runoffs need avoiding, due to their expense.
      Plurality needs them when lacking a majority, for we know they  
could not completely express their wants - and still have trouble.
      For others, need thought as to when they are worth the pain.

Primaries are another Plurality need - need thought as to when they  
are worth their expense elsewhere - and how to do them well.

Write-ins - needed, though need should be avoided at Runoff time.
>
> -Plurality: Everything. It routinely requires dishonest strategy  
> from a large minority, or even a majority, of voters. Enough said.

Does not let me express my desires - unless bullet voting was always  
good enough for all.
>
> -IRV: Voting can hurt you (nonmonotonicity). That means that small  
> third parties can survive, but once they threaten to pass 25%,  
> you're back to the problems of plurality. A great learning tool to  
> understand this is http://zesty.ca/voting/voteline/ , which lets you  
> play with one-dimensional scenarios and see how common  
> nonmonotonicity is.

Ballot is good, but counting too often ignores what is important.
>
> -Condorcet: complexity. While the basic idea of one-on-one matches  
> is simple, the details of tiebreakers are enough to make most  
> voters' eyes glaze over. Moreover, the need to individually rank  
> numerous candidates is more work than many are ready for, and the  
> inevitable shortcuts they'll take could harm results.

Ballot is good - rank only the candidates you like best, with best at  
top and equal ranking permitted.  Bullet voting is fine when that is  
your liking.

Some talk of voting for frontrunners - above sentence gives all the  
encouragement worth offering.

Its ballot is like IRV's - it is the counting that is more complete  
and smarter.

The counting, reportable as an N*N matrix comparing each pair of  
candidates, is valuable both to indicate progress and to help in  
deciding how to do better.

Tiebreaking is only a problem if you feel you need, but cannot get,  
adequate understanding.  It is simply a cycle of those most voted for,  
thus including the winner, separated from the less-liked rejects.
>
> -Approval: divisiveness. By forcing all votes into an all-or-nothing  
> mold, it does not allow partial alliances between candidates.  
> Consider the probable results in the recent Hawaii election, where  
> the majority democrats split their votes between two candidates,  
> leading to a Republican win. Lets assume for a second that, because  
> the two democrats were distinguished mainly by individual not  
> ideological factors, cross-party approvals are insignificant; and  
> that Democrats are pretty evenly split between the two choices.  
> Then, there are two possible results: either the less-cooperative  
> Democratic faction wins, or, if the "uncooperative arms race" gets  
> out-of-hand, the condorcet-loser Republican wins. In other words,  
> the system has incentives not to cooperate between two frontrunners  
> running approximately even in the polls, no matter how close they  
> are, and these incentives are unhealthy whether or not they get out- 
> of-hand.

This sits between Plurality, which supports only bullet voting, and  
Condorcet that provides for needed ranking of multiple candidates.
>
> -Range: Strategy is too powerful. If one faction is more inclined to  
> honestly rank, seeing themselves as neutral judges, while another  
> faction has selfish reasons to strategically vote approval-style,  
> the strategic faction will dominate, even if they are a minority.  
> Range is very robust under strategy, if it's not factionally biased;  
> but too vulnerable to factionally biased strategy. You can  
> rationalize until you're blue in the face about how minority Range  
> winners reflect a true societal preference; but imagine how you'd  
> feel if Bush/Gore/Nader had been decided for your least-favorite  
> against the will of the majority, due partly to a certain complicity  
> of some people who should should SHOULD have been on your side, and  
> partly to the obvious and dishonest machinations of the winning  
> side, and you'll see that this is still a real problem. (OK, I know  
> that doesn't take a lot of imagination for some people.)

The rating is a great ability, but trying to do it well is a major pain.
>
> -Bucklin: Bucklin (with equal rankings, of course) doesn't really  
> have a single biggest weakness. It is still technically just as  
> vulnerable to divisiveness as approval; but the trappings tend to  
> hide this fact, and so it shouldn't be as much of a problem in  
> practice. Still, it doesn't have any really strong points either.  
> It's not the best honest system like Range; it doesn't give a  
> Condorcet guarantee; and it's more complex than Approval, without  
> really fixing Approval's greatest flaw.

In a way, more complex than Condorcet, with Bucklin's complications  
not worth the pain.
>
> So, allow me to restate my favored single-winner system, which, I  
> think, avoids all of the major pitfalls above. I call it Approval  
> Preferential Voting (the acronym, APV, is I believe only taken by  
> American Preferential Voting, an old name for Bucklin; and since  
> this system could be considered a Bucklin variant, I think that's  
> just fine.)
>
> Voters rank each candidate as preferred, approved, or unapproved. If  
> any candidates have a majority ranking them at-least-approved, then  
> the one of those which is most preferred wins outright. If not, then  
> the two candidates which are most preferred against all others (ie,  
> the two Condorcet winners based on these simple ballots, or the two  
> most-preferred in case of a Condorcet tie) proceed to a runoff.

How do voters get to a similar measure of whether a candidate rates as  
approved?
>
> (As a ballot mechanic, parties as well as candidates could be  
> ranked, and any candidate not specifically ranked would default to  
> her party's ranking.)
>
> This method is very simple. I think that the description above,  
> without the parentheses, is simple and intuitive; it uses only  
> concrete terms. It is also very easy for a voter to sort candidates  
> into three rankings; I'd argue that this is the easiest possible  
> ballot task, easier in general than either two or four ranking  
> categories. (Two means too many compromises, and four means too many  
> fine distinctions.)

I understand ranking, as done for Condorcet, as doable since it is  
based on he voter's own evaluation.  I then wonder how to fit to  
categories such as the above.
>
> It's not quite the same as MCA or any other Bucklin system, since if  
> there are two approval majorities, the preferences, not the  
> approvals, break the tie. This makes APV more lesser-no-harm-like  
> than Bucklin, encouraging voters not to truncate.
>
> Note that APV is still not a lesser-no-harm method. But it is in  
> some sense a lesser-minimum-harm method; extra approvals cannot hurt  
> your candidates chances for an outright win OR for a win if there's  
> a runoff, the only way they can hurt is the unlikely situation where  
> they are pivotal in preventing a runoff. I think that this minimizes  
> the divisiveness I discussed with Range above; for instance, in  
> Hawaii, I'm sure the two democratic factions would have had little  
> trouble giving each other sufficient honest approval for the  
> strongest one to win outright.
>
> Also, if there is no runoff, this method "violates Arrow's theorem".  
> That is, because it does not use a preferential ballot (and thus  
> doesn't have "unlimited domain" by Arrow's terms), it satisfies some  
> Arrow-compatible definitions of the Majority Criterion and  
> Independence of Irrelevant Alternatives Criterion (including  
> clones). (APV as a whole does violates both those criteria, but I'd  
> argue that this would be unlikely in practice.)
>
> This system as a whole is monotonic (unlike most two-round systems).  
> Raising a candidate X can only help X win if there are already one  
> or more candidates with majority first-round approval; it can only  
> avoid a runoff if thereby X wins; it cannot knock X out of the  
> runoff; it cannot knock a weaker opponent out of the runoff (this is  
> the step where many two-round systems fail); and it obviously helps  
> in the runoff itself against any given opponent.
>
> It does technically fail the participation criterion; your vote  
> could knock your second-favorite candidate out of the runoff, thus  
> causing your favorite to lose to a worse candidate in the runoff.  
> However, this is pretty implausible, since, in order to knock out  
> your second-favorite, your favorite must demonstrate that he's  
> stronger than her in a Condorcet sense, which would strongly suggest  
> that he's more likely to win a runoff than her. (Even in the  
> extremely-rare cases where this wasn't true, it would be almost  
> impossible to know that was so based on polling; so this failure is  
> a very implausible basis for any strategy in any event.)
>
> The worst downside of this method that I can see is that, unlike the  
> voters, the leading candidates have little motivation (except  
> reciprocation) to express approval for other candidates. Negative  
> ads could still be the order of the day. But you can't solve  
> everything.
>
> I've advocated for the different aspects of APV before, but I  
> haven't presented (or named) it as a whole. I'd appreciate any  
> comments. Honestly, I think this should be the simple, practical  
> reform we're all pushing for, even as we argue and develop more- 
> complex systems with better theoretical properties.
>
> JQ
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