[Election-Methods] Corrected "strategy in Condorcet" section

[Abd ul-Rahman Lomax]

At 04:48 PM 7/31/2007, Juho wrote:

>>>The additional (utility/preference strength related) information that
>>>range style ballots provide is excellent information. The only
>>>problem is that we don't have a voting method that would both take
>>>that information properly into account and be resistant to strategic
>>>voting at the same time.
>>
>>I've suggested one. Why not consider it?
>
>I have given it some consideration. I think I have also commented
>this type of methods few times.

Juho, this is less than helpful. What do I search for, "it," 
"methods," "commented" and "few times"?

>>Problem is, they can make spectacularly bad decisions with people
>>voting sincerely! It's inherent in the Codorcet Criterion, which
>>utterly neglects preference strength, turning a fly's weight of
>>preference into something equivalent to life or death. (I.e., both
>>preferences are considered equally.)
>
>Could you present the concrete example where this happens.

The pizza election. If you don't like pizzas, think about them as 
political candidates, only more useful.

>  I actually
>just posted one example in my recent mails where the winning votes
>pick a candidate that doesn't seem to be a reasonable choice.

If I'm correct the information about the election is ranked votes. 
While you may be correct about this particular pattern of ranked 
votes, ranked votes convey very limited and quirky information, it 
can be good and it can be terrible. In the pizza election, let them 
vote ranked.

2: A>B>C
1: B>C>A

How much does this tell you?

Make it a range election:

2: A, 100, B, 99, C, 0
1: A, 0,   B, 100, C, 50

(In real pizza elections, it would be common that the bottom would 
not be normalized, except that in this one, the single voter, without 
normalization would still rate A as 0 because that voter cannot eat 
pepperoni, period.)

You can take the second set of ballot data and make it into the 
first. Look, it's obvious. A Range ballot collects more information, 
if the resolution is sufficient (Range 2 is like a 3-rank ballot, 
which is fairly limited, which simply means more equalities, Approval style.)

>  But
>maybe you see the world from the Range perspective and refer to some
>example where Condorcet picks a candidate with low sum of utilities.

No. I see the world. It is not Black and White. Everything is in 
shades, degrees. Artificial control systems can be black and white, 
it's primitive design. And sometimes Yes/No is very good, but only 
under certain conditions, where choices have been boiled to do Do 
This, or Don't Do This. As soon as you try to use binary choice for 
two candidates for action, you are really using trinary choice: Elect 
A, Elect B, or Don't Elect Anybody. Artificially, some systems 
exclude the third choice, which is quite clearly undemocratic. It is 
the past binding the present.

And for trinary choices, if you must make them all at once, summing 
utilities is the method of choice. This is for individuals as well as 
societies. We often reduce it by pairwise comparison, and, *usually* 
this is adequate, but it is far better to use a summation method 
first, use it to make a nomination, and make a Yes/No comparison on 
that. In other words, we might very well put A against B, but then 
vote Yes or No on the winner.

Anything else is a shortcut, and shortcuts are used for efficiency, 
they lose accuracy. And, unfortunately, the consequences can 
sometimes be large. Given that it really isn't necessary to take 
these shortcuts, most of the time, why do we do it? Inertia. That's 
about it. I don't think it is a deliberate plot to deprive the people 
of fair elections, I think that mostly those in power are not 
knowledgeable about these issues, they aren't even thinking about 
them. And they get burned too, sometimes....



>>Range is an excellent method for use in small groups as a poll, to
>>suggest a nominee. You wouldn't use Condorcet for that, not if you
>>know what is good for your group! You are going to ratify the
>>result anyway, small groups have the luxury of that, so the result
>>*must*, with good procedure, satisfy the *ultimate* Condorcet
>>Criterion.
>
>Note that I don't consider the Condorcet criterion to be the ultimate
>criterion (and I have told this to you about 5 times :-). In non- 
>competitive elections I'd be happy to use Range and allow a candidate
>that is not a Condorcet winner (the one that would beat all others in
>pairwise plurality elections) to win. Condorcet criterion is a good
>rule for competitive elections though.

But there is no necessary conflict, and if you think there is, you 
have not understood the proposals for runoffs. First of all, in the 
large majority of elections, we are quite sure, the Range winner is 
the Condorcet winner. It takes special preference patterns to cause 
the discrepancy.

Since you can determine a Condorcet winner from a Range ballot set, 
why not run a Range election, and elect the Range winner if that 
winner is unbeaten? To be strict, I'd even define on the ballots an 
approval cutoff and require that the winner have that approval from a 
majority to be elected unconditionally, *and* not be pairwise beaten.

In most elections, this will be enough, there will be no runoff. The 
Range aspect makes it scalable, I think, to large numbers of 
candidates, at least better than Condorcet, which can be lousy with 
many candidates, not to mention the nightmare of a ballot and the calculation.

However, it can occur, might occur in 10% of elections, rough guess, 
that there is someone who beats the Range winner pairwise, or there 
is no majority Approval Range winner. By not more widely approving 
candidates, the voters have decided, effectively, that it's worth 
having a runoff.

It's very simple, really, and matches existing law in many places. 
Start with Approval, similar rules. Add the Plus marker to indicate 
Favorite, simple to count, and useful for several purposes (campaign 
funding, etc.), and you can do pairwise comparison. Then, later 
reforms can add rating levels. Or ranks if for some strange people 
would prefer the resulting loss of information.

A range ballot indicates rank, fully, (with some caveats about 
resolution) but a ranked ballot has no preference strength 
information at all. A gnat's breath, a moment's whim, is quite 
equivalent to a dedicated, firm choice.



>>The Condorcet Criterion is problematic also because it can award
>>victory based on a small percentage of the electorate, the Majority
>>Criterion is much stronger. It's advisable, in my opinion, to never
>>award elections based on a plurality, period. The safest way to do
>>it is with a ratification, and we we really start to design
>>election methods both for efficiency and accuracy, we'll consider
>>that.
>
>A "small percentage" example would make thing clearer to me.

Many candidates. Is that enough?
34: A>B=C=D
33: B>C=A=D
32: C>A=B=D

A beats B 34:33. A beats C 24:33. 34% of the voters elect A with a 
Condorcet method.

Whether or not this is a good result depends on the utilities. It's 
probably a bad one, though, this electorate needs to work on finding 
better candidates. (The example is not intended to be realistic. But 
Condorcet methods can generally determine a winner without the 
consent of a majority, and with many candidates the scenarios where 
it can get much more realistic. And Warren's simulations show that.)

If I were implementing a Condorcet method, I'd want to do a runoff in 
the above election, between A and B. I'm not thrilled with that, but 
it's better than selecting A without a runoff. There is no good 
result for this election, looking at the ranks. But looking at 
utilities, we might see something quite different.

         A       B       C       D
34:     10      3       0       0
33:     0       10      0       0
33:     0       3       10      0
--------------------------------
         340     531     330     0

Looks pretty different doesn't it? Now, this set of Range votes is 
not equivalent to the set in the Condorcet election, but people with 
these utilities might vote that way. The Range ballot converts to

34: A>B>C=D
33: B>C=A=D
33: C>B>A=D

B does win pairwise. But only because the Range ballot picked up -- 
if they voted that way -- a distinction that the voters did not 
express in the Condorcet ballot, because they thought that a 
relatively strong preference for the Favorite over the next was not 
worth expressing. (I didn't have time to come up with a better 
example for this.) Essentially, to find an example, take a Condorcet 
cycle and increase the vote count for one pairwise election, so that 
one candidate wins. I think you will still have far less than a majority.

Under the runoff standards, there is a pairwise winner over the Range 
winner, so a runoff would be triggered between A and B. B would have, 
probably, a small edge in this runoff, because the preference of the 
A voters is weaker, they may not turn out in such numbers as the B voters.

now, if they vote Approval style, what do we get? We get a plurality 
election, the A voters win. Giving a big hit on the overall utility. 
I am assuming that all voters voted sincerely in the Range election. 
If not, it reduces to pretty much the same as Condorcet. If the A 
voters vote sincerely, while the B voters vote Approval, are the A 
voters "suckers"? Not if there is a runoff. A will be in the runoff, 
and they have a chance to elect A. If they don't care, well, there 
you have it. They don't care, they are not harmed enough by the 
election of B to justify the harm to the B voters from the election of A.

If the A voters vote Approval style, and the B voters vote sincerely, 
B still wins Range, by a decent margin. So the runoff remains between A and B.

The runoff forces, essentially, the majority to make a decision. Do 
they really want to elect their candidate, knowing, now, that it will 
lower overall satisfaction? If they insist, they are the majority, 
and they can do it. Of course, the C voters will now weigh in as 
well, some of them will vote as well, and now they will be giving a 
full strength vote to B. B has quite an edge, actually.

>It appears that most discussion on Condorcet and competitive
>elections focuses on making the Condorcet completion methods (or
>Condorcet related but not Condorcet compliant methods) strategy
>proof. There is too little discussion on which candidate would be the
>best to elect.

Right. But in order to answer that, you really need underlying 
utility information. In simulations and examples, you can simply 
assume it. If you want correspondence to real information, you could 
use utilities generated by IEVS. You can then predict, with various 
strategies, how voters would vote and then study how the method 
performs for maximizing satisfaction. If you like, you can use the 
Approval Criterion, but then you have the problem of defining 
Approval cutoffs. Defining an Approval cutoff as the mean between the 
candidates is making an assumption that my approval depends on who is 
on the ballot. My *vote* may depend on that.... but not my actual 
approval, and when we argue that the most people should approve of a 
candidate, we are begging the question, and riding on the cachet of 
"approval," when what we are really referring to is a vote.

Measures of satisfaction, same as utility, are less arbitrary and 
more accurate. I approve of A, but *how much*?

This has nothing to do with whether or not people vote sincerely. 
That point has been radically confused by some. It's a measure, and 
we don't measure it from the assumption that people vote sincerely. 
Rather, we assume the underlying utilities, then look at how people 
would vote from them, with various methods of converting preferences 
and preference strengths to votes.

>Concerning combinations of ratings and rankings I still feel that in
>competitive situations ratings can provide useful additional
>information and guidance but including the rating info in the
>selection algorithm is quite complex. One interesting example on how
>to use ratings in Condorcet completion is in 
>http://fc.antioch.edu/~james_green-armytage/cwp13.htm

It need not be complex if you have a runoff. It's *simple*. So I 
really wonder if Juho has actually considered the proposal. Sure you 
can use ratings in Condorcet completion, not a bad idea. If you 
assume you are going to have a Condorcet decision. "Condorcet 
completion" refers to resolving a Condorcet Cycle and has nothing to 
do with the far more common example that there is a Condorcet winner.

Mr Armytage-Green, one of my partners in crime with Delegable Proxy, 
proposes on the cited page (I fixed the URL) having voters vote a 
ratings ballot, analyzing it Condorcet, which I've been proposing for 
some time. I've been saying that even if you are going to pick a 
Condorcet winner, having the ratings information allows you to come 
up with a better understanding of elections. And, of course, it gives 
you a ready -- and simple -- means of picking a member of a cycle. 
Armytage-Green, instead of choosingthe very simple method, describes 
something much more complex, I don't know why. Simply adding up the 
scores on the ballot gives you not only a means of resolving cycles, 
it provides some measure of election quality. This method would still 
give the election above to A, but the people would then realize why 
they were so dissatisfied with the election. It would be obvious.

Instead, it should be done the other way. The election is Range, and 
full Condorcet analysis isn't necessary. Usually the Range winner is 
the Condorcet winner, and when the Range winner is not, it is quite 
unlikely, I think, that there are *two* candidates who beat the Range 
winner, so detecting Condorcet cycles isn't necessary, all we need to 
do is look for a candidate who beats the Range winner. That's only 
one set of comparisons, counting the Candidate > Range Winner pair. 
It makes all the counting simpler. If someone beats the Range winner, 
there is a runoff between the two. If there are two who beat the 
Range winner, you pick the one with the highest Range rating.... 
that's my current proposal, at least. Remember, there are good 
arguments for simply picking the Range winner....