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

[Abd ul-Rahman Lomax]

At 01:45 PM 5/26/2010, Jameson Quinn wrote:


>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.)
>
>
>The voters can easily not use them. Many didn't. This is 
>overprotecting voters, taking facility away from them in the name of .... what?
>
>In the name of reducing turkey-raising strategy to an absolute minimum.

Turkey raising is pretty stupid in a Range or Approval-like system, 
so one is cutting off good voting facility in favor of eliminating a 
foolish and almost certainly ineffective strategy. Again, in the name 
of .... what?

>
>First, I'd love to take full range data on the first election, 
>defaulting to 100/75/0 for preferred/approved/unapproved, to be 
>analyzed by Range, Condorcet, and Bucklin standards and published 
>before the runoff. And the runoff should allow approval-style 
>write-ins, in case that analysis shows that my method got it wrong 
>somehow. So it's not about reducing expressivity.

Hey, pretty close to my suggestion. Those range defaults are, in 
fact, what I suggested, but I'd add the 50% slot as (bare minimum) 
approval, corresponding to original Bucklin, which worked, and could 
handle lots of candidates, and, to allow neutral and unbiased range 
and condorcet analysis, 25% as an additional disapproved slot. But 
maybe it would be better to have balanced approved and disapproved 
slots. With Range 5, that would be:

Favorite
Preferred
Approved
Almost approved
better than worst
The worst (default, blank)

Or instead of the loaded 'worst," perhaps simply "Maximally unacceptable."

Or Range 3,

Favorite
Preferred
Not quite approved
Unacceptable.

But this doesn't allow much preference strength expression in the two 
approved classes.

>But let's look at the overall strategy for APV:
>
>First off, if nobody ever uses the middle rank, it's just approval 
>with a runoff if there's no majority. That's a good system. It 
>would, for instance, have handled Clinton/Bush/Perot or 
>Bush/Gore/Nader with nary a hiccup. But in the recent Hawaii 
>election, with two 30% clones who hate each other against a 40% 
>other, it would have gone into a runoff.

Two clones who hate each other is an anomaly, by the way. Something 
is wrong with the picture, they are not actually clones, or they are 
both unsuited for public office.

This is a situation where the middle rank (third approved rank) might 
find a majority. 40% for one is pretty high. That candidate only 
needs to get 10% from other voters, the supporters of the 60%. 
Remember that voters are not necessarily partisans. Two outcomes are 
possible here:

The supporters of the 30% clones hate each other as much as their 
candidates pretend to hate each other, so they lose, because 16% 
second choice voting rate among that group, for the 40% candidate, is 
not terribly high.

The supporters fo the 30% clones preferentially second rank each 
other's preference, even more likely in third rank in original 
Bucklin, because it gives them more chance for the favorite to win, 
expressing stronger preference. But still approving of both. If these 
really are clones, as described, that voting pattern would be 
expected. So one of them would win, and it might even be one of the 
rare multiple majorities. Or, they would pull into the lead, and both 
of them would go into the runoff. The danger of the runoff has to do 
with real preference strength and turnout. There is a risk that the 
40% candidate might win the runoff. From the stated preferences it 
might not appear so, which is, quite precisely, why I suggest that 
voting examples give preference strength (i.e., sincere Range) data. 
Ideally, it would actually be non-normalized absolute range, because 
the difference in absolute utility to the voter is what drives 
turnout. When that's high, high turnout, when it is low, low turnout.

>The basic strategies in approval/runoff are standard approval 
>strategy (vote for one of the two frontrunners and anybody better 
>than them), plus turkey-raising. I'll look at turkey-raising later, 
>but let's assume for the moment that it's not a big factor. So, we 
>have standard approval strategy for the top rank. That means that if 
>there's a clear CW and a clear Condorcet 2nd place, then the CW will 
>have the only majority. If that happens, great; you're done.
>
>Of course, that condition held in HI and there was no majority.

It wasn't approval, and, even more, it wasn't ranked approval, which 
allows clear preference expressing while still approving to avoid a runoff.

>  That's because if the two frontrunners are clones, supporters of 
> other candidates will see no reason to waste voting power choosing 
> between two equal-utility options, and so will consider them as 
> effectively being just one of the frontrunners. So that's the other 
> possibility: a HI-like majority failure. Call the clones A and B, 
> and the third candidate opposing both C. (In HI, C was Djou, who won.)
>
>At that point, standard approval with no runoffs just falls down and 
>gives the election to the true third-place winner.

You've set up two contadictory assumptions: clones, but their 
followers don't vote for the other clone. Those aren't clones in any 
ordinary sense, only in a technical sense that ranks them together 
because they are both preferred to C, by a set of voters.

>  One big yuck. Approval with runoffs needs a runoff to decide, and 
> the true Condorcet winner might not actually be in the runoff, so 
> the election might go to the true second-place winner. Two small yucks.
>
>How do you encourage voters to include additional rankings so as to 
>avoid a runoff in this situation? Standard Bucklin certainly does 
>not do the trick; the same 
>damned-if-I'll-cancel-out-my-own-vote-by-also-voting-for-the-second-frontrunner 
>logic applies exactly as much in the second ranking as it did in the 
>first! My later-minimum harm takes away this strong reason for A and 
>B voters not to extend their approval. But they still have no 
>particular positive reason to do so.

You think that this logic applies. Most voters did not follow that 
logic! You have also removed from Bucklin a device that real voters 
actually used to express maximum preference strength, to give their 
favorite the best chance to win in the primary: skipping second rank.
[...]
>...
>
>That brings us, finally, to the issue of turkey-raising. That is the 
>reason for restricting to three ranks. If you let people make fine 
>distinctions "for free", that is, with essentially no effect on a 
>first-round winner and only affecting who makes it into the runoff, 
>then that's basically begging people to think about turkey-raising. 
>(BTW, Abd, that's the problem with your idea of having distinctions 
>among unapproved candidates on a Bucklin ballot.)

I don't see it as a problem. I see those voting turkey-raising as, 
often, getting what they deserve: a result they don't like. The 
distinctions I suggested are only used to add, possibly, a third 
candidate to the runoff. So you think they will turkey-raise for 
that? That's fine, but it could very easily backfire. Runoffs are 
notorously hard to predict. That "turkey" might turn out to have a 
constituency that didn't even vote in the primary because they 
thought it would be useless. Get the candidate into the runoff, the 
situation flips. And, presumably, your goal as a turkey raiser in 
this case would be to get your two favorites into the runoff, not the 
real opposition. But your favorites may be perceived as front-runners 
then, and their supporters may stay home, thinking that it's a done 
deal. Boy, could they be surprised!

They got what they voted for.

This whole concept of hobbling voters so that they can't "do bad 
things" is completely backwards. Trust the voters! Give them tools to 
express their preferences, accurately. Then make the method 
*reasonably* strategy-proof. Remember, Bucklin is basically approval, 
and we are just adding some tweaks to deal with unusual situations: 
multiple majorities, perhaps, or, more likely, majority failure, as 
well as the ability to detect a Condorcet winner. And then, if these 
choices do need to be made -- which is unusual! -- a runoff.

>In my system, however, where would people raise a turkey? By voting 
>for them as favorites? Besides going against human nature, this is 
>extremely dangerous; it is likely to elect the turkey outright or to 
>knock your favored candidate out of the runoff. By approving them? 
>Again, this is a self-limiting strategy. For it to matter, it must 
>mean that there is a runoff; but then, the more it's used, the more 
>likely it is to simply elect the turkey outright. (It would be safe 
>if there were expected to be one or more majorities and no runoff; 
>but then it would be irrelevant.)

By the way, you might notice in my sequence of suggested reforms, 
that the first reform is simply Bucklin, 3-rank, and even the 
allowance of equal ranking in first and second rank is a minor 
extension, it fixes certain problems. It makes it *easier* to vote 
*sincerely*, not harder.

>**Yes, I could have used a Condorcet logic to resolve the multiple 
>majority, as I did to decide who goes to the runoff. It would even 
>have made this method satisfy the Condorcet criterion for honest 
>voters. But I think that multiple majorities will be rare, and that 
>when they happen, top preferences and Condorcet will give the same 
>answer, so I went with the option that simplifies explanations and 
>rapid counts.

The first implementation would not have, I'd assume, Condorcet 
analysis as part of the method. Range analysis is easy, just add up 
the votes, assigning them values. Condorcet analysis requires more 
work, though since it only needs to be a test against the straight 
Bucklin and/or Range winner, it isn't bad.



>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.
>
>
>Not a tie, Jameson. Multiple majorities, quite a different things.
>
>
>How do you say it, then? "Break the multiple majority"? "Decide the 
>multiple majority"? "Decide the issue"? "Resolve the multiple 
>majority"? I guess the latter, but we should agree on terminology. I 
>was trying to use "tiebreak" as the right verb here, but you're 
>right, it's imprecise.

Just understand that there is already established precedent for 
resolving multiple majorities: the choice with the most Yes votes. 
The described breakdown of this method, where a 51% majority defeats 
what could be 100% approval, is a clue. Once 100% approval data has 
been collected, there would be a cry of outrage from the 49% that 
just got aced out, and, my guess, some of the 51% would have said, 
"this isn't what we intended."


>As was pointed out, this rule (if multiple majority, the highest 
>first-preference vote prevails) leads to proposterous conclusions, 
>i.e, to make it completely extreme, one candidate has 51% approval, 
>but leads in first preferences (say it's a plurality, and this can 
>be quite small, overall), and the other has 100% approval, but the 
>51% candidate wins, through the rule about first preferences.
>
>
>Yes but:
>
>In reality, multiple majorities were rare with Bucklin, the problem 
>tends to be in the reverse direction, no majority even after all 
>rounds are collapsed.
>
>
>Exactly! This system is designed to best resolve the common case - 
>encourage majorities by not encouraging truncation - and not the 
>rare case of multiple majorities. It's a trade-off.

But a trade-off for what? Multiple majorities *did* occur; my sense 
is that they probably became rarer as people learned how to vote more 
effectively (which doesn't mean that the early results were poor, but 
if you are getting multiple majorities, it probably means that people 
were too-rapidly lowering their approval cutoff. The poor simulations 
of Bucklin were defective because it was assumed that the voters 
would simply rank, instead of understanding that Bucklin ballots are 
really range ballots and effective strategy is to vote them that way 
(but it's a little more complicated than that. The ballots are 
normalized within the approved class, and how the approval cutoff is 
determined is another question.)

>As mentioned above, using a condorcet analysis of the three-rank 
>ballots to resolve majorities, with first preferences only as a 
>fallback, would resolve your issue. I like that system; it's better 
>theoretically than the one I proposed. But while you can hide the 
>rules for getting into a runoff in parentheses, you can't hide the 
>rules for an outright win there. Basically, I came down on the side 
>of having a simple three-sentence description, with all concrete 
>terms; and of making the one-round-win calculable with any 
>vote-counting technology on the planet. (On the other hand, an 
>election-night announcement that "there will be a runoff, it will 
>probably be between X and Y but we'll tell you for sure who's in it 
>in two days" is something most people could live with.)
>
>My own solution to the multiple majority problem is different and 
>more comprehensive, without creating this preposterous conclusion of 
>rejecting a candidate clearly approved by all the voters, in favor 
>of one who might be quite divisive.
>
>
>Your solution also requires a course in voting theory to even 
>explain, much less understand. I support it nonetheless. Do you support mine?

Not comparatively. If it were on a ballot question, probably. Would 
depend on context.

I don't mind if a course in voting theory is needed to figure out 
what the best system for a jurisdiction is. (It can vary!). I do mind 
if a course in voting theory is needed to vote a good, reasoanbly 
strategic ballot. "Strategy" isn't "bad." It is a way that voters 
seek to express their preferences to maximize their personal utility. 
A good system will then use the data generated to attempt to 
maximize, from it, overall social utility.

The wild card here is Condorcet analysis. I'm on quite solid ground, 
I think, with both Range and Bucklin analysis, they converge, and 
they will only rarely differ, I expect. As to turkey-raising with 
Range analysis, the most they would give the "turkey," unless they 
actually approve the sucka, would be a quarter-vote. My sense is that 
if we could read the mind of the voters, turkey-raising would be 
extremely rare. It would encourage turkeys, is this what the voter 
really wants to do? Next election, even if not this one, that turkey 
might win because those votes help create an appearance of viability, 
and sometimes appearances turn into realities. It's like polls. If I 
were asked what I think about Sarah Palin, would I say, "Great! if 
she's running for president in 2012, I'd vote for her for sure. You 
betcha!" Hoping that this would convince the Republicans to nominate 
her? Wouldn't I be setting myself up for huge regret later on? "Oh, 
my god, I talked to all my friends and we spread this viral message 
to answer this on-line poll that Sarah Palin was about perfect, and 
that allowed her to raise the funding and make a real run, and the 
country had turned just enough to elect her! What have we done? Why 
didn't we put our efforts into improving the voting system and 
supporting good candidates? Honestly."

I'll tell you, the "it has to get worse before it gets better" -- 
which was common among Nader supporters in 2000 -- is an argument 
that has resulted in some true disasters. It was actually the belief 
of Charles Manson, for an extreme example. And he "voted" to make it 
worse, so it could get better quicker, he thought.

So, would Condorcet analysis encourage turkey-raising? I don't know, 
and I'm not sure that anyone knows. We have a lot of "theory" and not 
much experiimental practice. With a Bucklin runoff, turkey raising 
*might* impact SU, but not as much as other election pathologies 
already do it. The issue is whether or not preserving the condorcet 
criterion, which in this method would be easy to understand, not 
difficult, is worth the trouble and risk (presumably the risk of 
turkey-raising).

The definition here would be something like the following.

Ballot: I'll assume four-rank: three expressly approved ranks and one 
disapproved rank that is preferred over other disapproved candiates. 
The last rank is only used if needed to make certain checks, and may 
affect whether there is a runoff or not, and the identity of the 
candidates on the runoff ballot.

Two variations:

(1) If a majority is found in the primary, the election will 
complete. The presumptive winner is the candidate with the most 
votes, but if there is another candidate who, from the rankings, is 
more preferred (would win a virtual pair-off), and if this candidate 
is also approved by a majority, that candidate wins.

a variation would do this, or also do this, with the Range winner, 
but none of these would, in early implementations, elect without 
explicit majority approval.

(2) If only a single candidate gains a majority in the primary, that 
candidate wins. If more than one candidate gains a majority, the 
presumptive winner is the candidate with the most votes, but if there 
is a candidate who is more preferred, from the rankings, than this 
candidate (more voters prefer the second candidate than the reverse), 
there is a runoff.

similar might be done with Range winner.

Then, if there is no majority in the first poll, there will be a 
runoff election. The candidates in the runoff may be up to three: The 
most-widely approved candidate (most approvals), the candidate with 
the highest sum of rating values (1 vote, 0.75 vote, 0.5 vote, 0.25 
vote, and the default 0 vote of no rating), and a candidate who beats 
both the others as described above.

If all three "leaders" are the same candidate, i.e, there is no other 
pairwise winner, then, good question: should a runoff be held? I'd 
say yes. Majority hasn't been shown. Later, it may be possible to 
determine from the ballots if there is any reasonable possibility of 
a different result than simply picking this one candidate, but I'd 
leave that for later.

Remember, we are here building on an already existing top two runoff 
system. We already know that these people want to find a majority, 
and are willing to go to some expense and trouble to get one.

Condorcet failure is a commonly asserted complaint about 
Approval/Range/Bucklin. This hybrid beats it with a stick. The only 
condorcet failure possible is one based on unexpressed preferences, 
which is one reason why more ratings are allowed, to make that less 
likely to be an issue. If there are as many possible ratings as 
candidates, that theoretical objection goes away.