[Election-Methods] Corrected "strategy in Condorcet" section
Juho
juho4880 at yahoo.co.uk
Wed Aug 1 13:59:19 PDT 2007
On Aug 1, 2007, at 5:37 , Abd ul-Rahman Lomax wrote:
> 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"?
True, but there was no specific question so I didn't know what to
say :-). Maybe my comments below cover some of this.
>
>>> 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.
Ok, strength of utilities ignored. That is typical to Condorcet /
ranked ballots. There is no intention to make bad decisions. Id say
we are talking about the recognition of the fact that opinion
strengths are too hard to measure reliably in competitive elections
and therefore they had to be left out.
>
>> 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.)
Yes, as noted many times, Condorcet ignores preference strengths, and
the best explanation is that it does no because they are too
difficult to measure (or actually - to take into use) reliably in a
competitive election.
(My example had a different viewpoint to Condorcet failures => making
wrong decisions when basing the decisions purely on the given rankings.)
>
>> 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.
I'd be disappointed in Range if it would always elect the Condorcet
winner.
>
> 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.
Note that when comparing A and B 34% of the voters preferred A, 33%
preferred B, and 32% said they are equal => we can say that 100% of
them indicated their opinion. This is btw not very Condorcet specific
- Approval, Range and others also allow the voter to be neutral with
respect to some pairwise comparisons.
>
> 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 have no idea why the voters should not mark this preference in
their ballots. I think the basic rule (in the absence of strategies)
in Condorcet is to express one's sincere opinions.
> (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.
Out of the possibilities that you discussed on how to combine Range
and Condorcet I find the scenario where ranked votes are derived from
the ratings to be the most interesting one. That method may carry
some (relatively sincere) additional information that may be useful.
Note that if there will be a runoff between the Condorcet winner and
the Range winner voters may become very strategic. If there is for
example a preference cycle A>B>C>A the A supporters probably want to
make sure that, if there will be a runoff, A will meet C and not B.
This will of course make the ratings more insincere. It could be also
difficult to decide whether to vote e.g. A=100,B=1,C=0 or
A=100,B=0,C=0. For these reasons the "informative" use of Range seems
more tempting to me.
>
>> 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....
I looks like the normal Approval strategy would apply. I'll skip
analysing this proposal in detail now (the mixture of Range, Approval
and Condorcet opinions is a rather complex equation).
Juho
>
___________________________________________________________
All new Yahoo! Mail "The new Interface is stunning in its simplicity and ease of use." - PC Magazine
http://uk.docs.yahoo.com/nowyoucan.html
More information about the Election-Methods
mailing list