[Election-Methods] Improved Approval Runoff

[Abd ul-Rahman Lomax]

At 07:01 PM 8/19/2007, Peter Barath wrote:
>Which means that the concept of "two candidates with the best chances"
>depends not solely on the candidates themselves but theoretically
>possibly on the voting method too!

Yes. Of course. But I don't think that voting 
method results in a different estimation of who 
is in the top two or three, which is all that is 
relevant in nearly all real-world situations. 
Let's leave out the California gubernatorial recall....

>In your example with 47 percent firm Bush supporters the voters
>were very wrong in supposing that he is a harmless candidate.
>In reality, in this case the strategic votes would be identical
>to the honest ones.
>
>However, I think your example did point to a widely ignored fact:
>that the ugly dilemma of the Plurality vote: "how will other
>voters vote?" does exist in Approval, even if it's smaller

It's not widely ignored. The question of how to 
vote in Approval is certainly not as simple as 
"Which candidates do you approve of?" However, it 
is quite a reasonable way to vote in Approval to, 
quite simply, answer the question sincerely, for 
yourself, and vote for those candidates. It is 
not necessarily strategically optimal. But what 
is the penalty for failure? One suboptimal vote is not much to worry about!

>So it's plausible to mix Approval.

Absolutely, this does not follow from what was 
stated. For one thing, "Approval" is absolutely 
the simplest, cheapest reform on the table. 
Simply Count all the Votes. Few among us consider 
Approval the best method, though there are, in 
fact, some experts who do. It's a respectable position.

However, there is no doubt but that Count All the 
Votes -- the name "Approval" greatly confuses the 
issue -- is a vast improvement for no cost. Sure, 
when you have a third party candidate who 
approaches parity with the big two, i.e., there 
are more than two frontrunners, strategic issues 
arise again. However, they do not bite as badly.

And they bite even less in Range. The choice 
becomes more difficult in Approval merely because 
the method is so black and white, so ... binary.

>  My favourite (at this moment)
>is a preference ranking with an approval cutoff. For me it's
>interesting enough that it can be used in two ways:

Well, I've been suggesting the reverse: Approval with preference indication.

>1. If there is a Condorcet-winner she/he/it wins. If there is
>    not, the Approval winner wins.

Sure. That's been proposed many times. However, 
it's not a very good method. First of all, it is 
blatantly obvious, if you care to look, that the 
Condorcet winner is sometimes *not* the best 
winner, by far. Secondly, if you *do* think that 
the Condorcet winner is the best, if one exists, 
one would think that, if there is a cycle, that 
the winner should come from a candidate who is a 
member of the cycle, and not be an Approval 
winner, who would have been beaten by any member 
of the cycle. So if you really want to go this 
way, you use approval level to determine which 
member of the cycle wins. And I don't know what 
this is called, but it is certainly a known method.

However, consider the reverse, and, while we are 
at it, we might as well use a Range ballot. Range 
ballots need be no more complicated than ranked 
ballots, but they provide more information. You 
can do preference analysis on Range ballots, but 
not range analysis on Ranked ballots.

It is already established practice in many 
places, when there is no majority preference 
shown in the election, to hold a runoff. What is 
generally done is that the runoff is between the 
top two. And, of course, this is just like IRV, 
except better. And more of a nuisance, hence the 
idea of combining the runoff with the first 
election.... But my point, really, is that certain conditions trigger a runoff.

Now, Range is the only method on the table that 
considers true preference strength. Some 
Condorcet methods use a presumed measure of 
preference strength, but there is no reliability 
to it at all. In any case, in simulations, Range 
outperforms nearly all other methods in 
optimizing overall voter satisfaction with the 
result; it essentially does this by using 
*expressed* expected satisfaction! Some claim 
that this makes it vulnerable to "strategic 
voting," but the term is actually misapplied to 
Range, in part because there is no fixed 
algorithm for converting sincere preferences and 
internal absolute utilities to specific Range 
votes. Essentially, what I've come to, is a Range 
vote is a *vote*, i.e., an action, not a sentiment.

And the simulations show that even if voters 
"strategize" to their heart's content, Range 
still outperforms other methods. *On average*. 
You can always come up with specific scenarios 
that will make it appear otherwise, but what I 
find fascinating is that, so far, all such 
scenarios I have seen depend on contradictory 
assumptions. A voter has a weak preference, i.e., 
does not care much which of two candidates wins, 
but votes a strong preference, supposedly to make 
his favorite win. I.e., votes as if he cares. Why 
would he do that if he does not care? He *does* 
care, he wants his favorite to win!

There is absolutely nothing wrong with that. What 
I would like to see, in Range, is that voters 
vote to optimize their own expectations. If that 
means voting Approval style, fine! However, from 
what I've seen in my own limited work, it appears 
that the presence of even a few voters casting 
intermediate votes improves the expected outcome for *everyone*.

Now, Range Voting does *not* always fully 
optimize overall satisfaction, for various 
reasons. It is *not* perfect, for a number of 
reasons. For one thing, there is no reasonable 
way for voters to vote absolute utilities. 
(Someone might prove me wrong, someday; for 
example, if voters' votes are bids, where they 
have to pay if they get what they want, we might 
assume that the votes will be reasonably accurate 
... this would, in fact, be tax reform as well as 
election reform; I'm certainly not taking on this 
project at this time!) Instead, what we expect 
most voters to vote is normalized utilities, 
normalized to the candidate set. This distorts 
absolute satisfaction, equating what might be a 
weak preference range for one voter with what 
might be a strong preference range for another.

In any case, one of the situations that can 
happen with Range is that the preference of a 
majority fails to win. This is sometimes used as 
an argument against Range, but it is actually a 
strength, that such a situation is possible, 
because once you look at preference strength and 
its implications, it is obvious that an ideal 
method would not satisfy the Majority Criterion.

However, there is one aspect to the MC which is 
very important: it resembles the principle of 
majority rule. It is *not* majority rule, 
because, quite simply, the majority may sometimes 
decide -- by majority vote -- to choose other 
than its own first preference. However, a 
single-stage election method, where the 
information is gathered that might lead a 
majority to make a choice like that, cannot 
clearly allow this. Technically, a majority 
could, on the ballot, consent to the winner being 
the Range winner, but that is an a priori 
consent, which is problematic. "But I didn't 
realize that it would be ...." It is not full, 
clear consent, and the consent of a majority is a basic principle of democracy.

Hence my proposals: first of all, a range ballot. 
We really should start using range ballots, even 
if we only analyze them, to determine winners, as 
ranked ballots. I.e., take a set of ranks and 
allow overvoting at any rank, and undervoting in 
others. Even if the election is, say, a Condorcet 
method, it them becomes possible, particularly if 
the voters understand what is going on, to 
analyze them to study the effect of Range.

But as an actual method, use such a ballot, 
determine the Range winner, and then consider if 
any candidates beat the Range winner in 
preference analysis. If so, hold a runoff. In 
most cases, the Range winner will be unbeaten, 
but it is the exceptions that are interesting. 
(Range, like Approval, usually finds the 
Condorcet winner if there is one). If the Range 
winner is beaten, it would be rare that there are 
two who so beat the Range winner, so I'm not 
going to, at the moment, go into how to resolve 
this, whom to include in the runoff. But I do not 
consider it a difficult problem, and it has very 
little effect on strategic considerations, 
because we can expect it to be a very rare consequence.

Suddenly, we have Range being MC compliant, as to 
the overall method! And it really is only an 
application of existing practice, modified to 
meet the somewhat new circumstance of something other than top-two plurality.



>2. Calculate the two candidates with the most Approval points
>    and the pairwise winner of them wins.
>
>Peter Barath
>
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