[Election-Methods] Improved Approval Runoff

[Abd ul-Rahman Lomax]

At 01:29 PM 8/16/2007, Diego Renato wrote:
We should resist TACTICAL bullet voting for the same reason that many 
other methods than plurality. Increase the overall satisfaction of the voters.

It's an error. The one most harmed by "tactical" bullet-voting is the 
voter who votes that way. Some analysts are confused by the fact that 
it can look like tactical voting is advantageous. However, what it 
boils down to is like this:

You are the last voter. By some process, you know how everyone else 
voted. There is a tie between two candidates. You approve of both of 
them. How should you vote?

Well, you have a choice. You can vote for both, and thus let, 
usually, chance determine between them, or you can vote for your 
favorite. The choice is yours.

And, indeed, this is the situation with voting, properly: the choice 
is yours, as a voter.

If a so-called "tactical voter" supposedly approves of two 
candidates, but only votes for one, we must look at why. Let me 
suggest why: the voter has a preference, and the preference is strong 
enough to motivate the voter to bullet-vote. There is a contradiction 
in the assumptions: weak preference is assumed if we think the voter 
approves of two, and strong preference in the action of voting.

The voter has a reason for voting that way! He wants his favorite to win!

And there is *nothing* wrong with this.

We suggest that the proper way for each voter to vote is to increase 
his or her own satisfaction. And then we try to use methods that take 
this information, and use it to find the winner who will satisfy the most.

If the voter conceals relevant satisfaction information, then the 
method will not know how to satisfy this voter! And it may err, with 
regard to this one, and thus to the overall satisfaction. We must 
note, that if this "strategic voter" prevails, and the candidate 
wins, that candidate must have been also approved by others. We may 
argue that if the voter had also voted for another candidate, that 
the winner might have changed, and this might have resulted in more 
people being satisfied. But it is just as likely, unless the voter 
has the kind of knowledge described above, that the voter who bullet 
votes ends up with a candidate that the voter is not satisfied with.

When I studied the specific outcomes in a Range 2 election (ratings 
of 0, 1, 2), what I saw with bullet voting as distinct from so-called 
sincere voting was the same expected outcome, *but* greater 
variability. That is, sometimes bullet-voting caused the favorite to 
win, a desirable outcome for the voter, but sometimes it caused the 
least-favored to win, because the voter did not also approve of the 
middle candidate. As I recall, there was one scenario (the study 
looks at all possible pre-vote scenarios where the voter's vote can 
affect the outcome) out of 27 where a sincere vote resulted in a 
worse outcome than bullet voting, and one where it resulted in a 
better outcome. Looking at approval style votes, in particular bullet 
voting, there were two scenarios where the voter gained by bullet 
voting, and two where the voter lost.

This was a zero-knowledge election.

What has happened is that far too many analysists have not taken a 
close enough look at the actual scenarios, at what actually happens 
in voting, but instead they rely on superficial analyses and specific 
examples that make it look like the strategic voter gains something 
unjust. But the strategy used only makes sense in certain contexts, 
and the risks of that strategy, in that context, are not considered 
by the analyst.

 From what I've seen, the regret of the strategic voter whose 
strategy fails is deeper than the regret of the sincere voter who 
loses some value because of voting sincerely. If you give a candidate 
some support, but not enough, because you had a favorite you wanted 
to reserve the full vote for, you may regret it, but you know that 
you were, at least, sincere, and the result turned out differently 
simply because others did not agree with you.

But if you fail to vote at all for someone you really would prefer to 
the one who wins, you may kick yourself for a long time..... why 
didn't I just express what I felt?

But if the voter really did express how he felt, if he really 
*didn't* want to vote for that candidate, then his vote was sincere, 
it was not a strategic vote.

We set up a contradiction when, in Range and Approval, we assume weak 
preference in a context where the voter indicates a strong one. 
Suppose you are out with friends, and you are choosing a pizza.

(Oh, no, here comes the pizza election again!)

Your friends say they prefer Pepperoni, but Mushroom is okay with 
them. You are the last voter.

Suppose you are Jewish, keeping kosher, you can't eat Pepperoni. (I 
think some Jews will have other problems as well, with food not 
prepared in a kosher kitchen, but lots of Jews aren't that strict, 
but they won't eat pork.)

You will say so, presumably, you will indicate maximal preference for 
Mushroom, and you will all have mushroom

But suppose you were lying. You really don't keep kosher, it was just 
an excuse, and you have a slight preference for Mushroom, that's all. 
And you don't care about the others getting their preference, even if 
there are two of them and only one of you. You want it for yourself, 
you are selfish. (You might also want to pretend to be keeping 
kosher, which is another issue, one which I would call strong 
preference, it's just not about pizza but about something else.)

So you say the same thing.

And then the guy at the counter says, oops! We ran out of Mushroom. 
What about Pepperoni?

What I've concluded is that we should generally consider that voters 
vote sincerely, but that "sincere" is not at all obvious, there are 
many motives that go into it. Many analysists simply assume certain 
utility numbers, and then assume that those numbers would translate 
"sincerely" into votes in some fixed way. It's a drastic 
oversimplification of the system. It's possible to work with 
simulations where we have something like known sincere absolute 
utilities, but there is not only one way to translate these utilities 
into votes.

The best overall results are found, indeed, if everyone votes 
sincerely, meaning that the way they vote actually expresses how 
satisfied they would be with each outcome; however, there are lots of 
reasons why it might not be that simple. Further, to me, majority 
rule requires, where possible, that the majority consent to anything 
other than its first preference, explicitly. Single step rules cannot 
both satisfy the Majority Criterion and social utility maximization; 
forced to choose, I would choose SU. Since that really is the goal, 
properly, and the majority would only lose its first preference if it 
loses little, whereas the minority loses more if it loses its preference.

However, it is possible to have the Majority Criterion and the cake 
as well. We can have SU maximization and then test that the majority 
accepts the result -- "prefers it" -- over its original preference. 
The easy way, with Range, is to analyze the ballots for preference, 
and see if there is any candidate who would beat the Range winner 
pairwise. If there is, a runoff is held.

(It is actually rare, Range usually chooses the Condorcet winner, not 
to mention the Majority winner, it takes special and unusual 
circumstances to create majority failure in Range. So, if there is 
majority failure, it would be even rarer that there is more than one 
candidate who pairwise beats the Range winner, so, my suggestion is 
that a runoff take place under two circumstances. If there is a 
pairwise winner over the Range winner, the pairwise winner faces the 
Range winner in a runoff. If there are two or more such, and there is 
a Condorcet winner among them, the Condorcet winner faces the Range 
winner. In the extraordinarily rare circumstance that there was a 
Condorcet cycle beating the Range winner, the member of the cycle 
with the highest Range rating would face the Range winner in the 
runoff. And the final condition (the above being variations on the 
pairwise situation) is that there is an Approval cutoff specified in 
the election, perhaps 50%, and no candidate got 50%, and there is no 
pairwise victor over the Range winner. In that case, the top two 
Range winners would face each other.

Range with top two, which is simply that, I think, unconditional 
runoff, has better SU results than pure Range, in the simulations.



>I'm not sure I understand the "second round." The expression was a
>bit garbled, I suspect. I assume that the "second round" is not an
>actual runoff, but a recounting. As written, it would seem manifestly
>unfair to the first candidate, the plurality winner of the approval election.
>
>
>It is a runoff.

With an actual runoff, we can get very good results, very close to 
optimal from the SU perspective, in a much simpler fashion.

>I'm not well informed about Asset Voting, but in Brazil, where 
>two-round elections are performed for single-winner elections, there 
>are negotiations among candidates for influence the support of the 
>voters during the second round. Frequently voters do not vote for 
>the supported candidate of their first round favorite.

That's correct, and it would be here too. However, this isn't like 
Asset Voting. What is different with Asset is that you really can 
vote for the person you most trust, of the whole set of everyone 
willing to serve at least as an elector. When you are voting in an 
election, sometimes you will vote for someone you don't really trust, 
but simply because you think you will get a better outcome, 
considering what is on the ballot. A vote in standard elections does 
not tell us much about whether or not the voter trusts the one 
getting the vote, and that's the issue about voting as recommended.

In Asset, because votes are not wasted, a vote *does* indicate trust. 
Asset gives power to the candidate, power either to be elected or to 
choose, according to the votes they receive, who will be elected. So 
the issue is trust, far more than party, platform, etc. The latter 
will be important, but pale in comparison to trust.

Now, consider this: if you are actually elected, what you are going 
to do, a lot, is to delegate authority. As a legislator, you will 
hire staff, you choose them, and they actually do much of the work, 
including research. Choose badly, you will perform poorly as a 
legislator. I'd suggest that a good legislator should be able to 
choose well. And, thus, if the legislator is *not* elected, that same 
person should *still* be able to choose well. If I would not trust 
someone to merely choose a winner, why would I trust that person *as 
the winner*, for that person is not only going to be elected with my 
vote, they will then vote on many matters with impact.

It really is the same issue, confused for us by the fact that we are 
accustomed to not having any significant freedom in choosing those 
who supposedly represent us. I'm claiming that if I can't *choose* my 
representative, I'm not represented, period. Asset allows me to 
choose my representative *to the election*, who might also be a 
candidate, or who might not, might just be someone willing to be a 
public voter. It might even be me, I might vote for myself, and then 
I participate in the negotiations to create winners. With only one 
vote, I might not get a lot of attention, so I will probably seek 
others with views similar to mine and cooperate with them. In short, 
I might name a proxy, and so Asset Voting readily becomes, 
informally, Delegable Proxy.