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

[Abd ul-Rahman Lomax]

At 04:59 PM 8/1/2007, Juho wrote:

> > 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.

My point. However, not that in a deliberative context, in a 
small-society context where people know each other and most activity 
is cooperative, plurality works quite well. People don't actually 
choose pizzas by Range Voting. They talk about it. And they make the 
decision, generally, that Range Voting would suggest.

If they are stuck, and they use standard deliberative process, which 
they can do because they are a small gropu (up to a few hundred 
people), the get the Condorcet winner, quite easily. With even better 
and simpler than Condorcet: Yes/No voting on a motion to elect a 
specific nominee.

The problems arose when the simple voting that was done in 
organizations, of holding a plurality poll, and then ratifying the 
winner (which requires a majority Yes), was replaced with Plurality. 
Moving to Condorcet, clearly better, but not as good as full 
deliberative process.

Range is not as good as full deliberative process, but it is much 
closer. The only difference, really, is that preferences will shift 
in deliberative process, and it's a little harder to stand up and 
claim, as you could by your secret ballot vote, that your favorite is 
a saint and the opposing candidates are devils, whereas you can do 
this with a Range Vote, more or less.

Essentially, if my hypothesis is correct, we had available, in 
assemblies, deliberative process. So when we started to have public 
elections, we just use the same shortcut that had been used in 
assemblies to speed it up: a plurality poll. In assemblies, there was 
a safety device: ratification, the acceptance by the assembly of the 
result. In a democratic assembly, the clerk may certify the vote, but 
that does not automatically complete the election, at least not in 
the process that I'm familiar with. It would go quite rapidly, 
routinely, the chair may say, "Without objection, the report of the 
clerk is accepted as the result of the election, and so and so is 
elected chair." And the chair will pause for something like a second. 
Unless the chair expects trouble. Then the gavel will come down and 
it is done. Except that the more complete rules do allow an objection 
if it is "timely," and, in particular, anyone can object to an action 
of the chair, so it's not totally over. The chair, properly, has no 
power at all, but is delegated the power of the assembly to act *with 
its consent* to make things more efficient. The assembly can withdraw 
that consent at any time. We saw in Texas recently a whole 
parliamentary brou-ha-ha where the chair refused to receive a motion, 
ruling it out of order -- it was motion to remove him as Speaker -- 
and he has the authority to do that -- and then he refused to hear an 
Appeal from a Ruling of the Chair, which was timely made. And then he 
declared the meeting Adjourned.

The latter two actions were entirely outside the rules, and the 
Assembly could simply have refused to Adjourn. The standard procedure 
-- it's not like none of this every happened before -- would be for a 
member to rise and, noting that the adjournment did not receive the 
consent of the assembly, nominate someone to act as Speaker Pro Tem. 
This member rising is acting as a very temporary chair.... the 
process would be pretty short, and a Speaker Pro Tem would then 
proceed with the business. In this case, the assembly would probably 
have declared the office of Speaker vacant and would have proceeded 
to elect a new one.

Anyway, my point is that deliberative process is fully democratic, 
election methods are a shortcut which is fine as part of full 
deliberative process, and risky as the actual decision-making tool. 
And all this probably escaped the notice of our early government. 
It's just what they did.

>  There is no intention to make bad decisions.

Of course not. It's the system, stupid!

>  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.

But exactly the same thing can be said about ranked votes. Why do you 
assume one is sincere and the other is not?

In any case, this was never the argument. There wasn't any argument. 
Juho is making all this up. It didn't happen that way. Range was not 
considered. At all. It would be interesting to find the first mention 
of the technique. And any evidence that I'm wrong, that it was 
actually considered (because some theorist may have described the 
method, but it was never actually considered by anyone with power.)

In any case, Approval is very old. And it's a Range method, just the 
most primitive. Borda Count is pretty old, but it isn't quite Range. 
It insists, I think, on equal preference strengths, so it's really a 
ranked method which simulates Range to some degree if there are a lot 
of candidates. Otherwise it's pretty messy.


>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.

But it's easy to collect the voters stated preferences and strengths, 
it is not difficult at all. Nor is it difficult to use the 
information; Juho's argument is circular.

We take voters word as to their preferences, why not their preference 
strengths?

Please, I haven't seen one argument for doing this here. The argument 
I've seen is that voters who vote intermediate votes are stupid, and 
that cunning Approval style voters will take advantage of them.

I find it a tad hard to accept this argument because it defines me as 
stupid. I'd expect that would, for *some* candidates, in *some* 
elections, vote intermediate votes.

With any election, the votes may not be "sincere." It doesn't matter. 
We take elections as actions, not as testimony. The voter acts to 
elect these, and acts against the election of those. So far, 
Approval. With intermediate votes, the voter continues with the votes 
just described, for usually at least two candidates, an then can act 
to elect a middle candidate over a last, but at the cost of risking 
the election of the middle over the favorite.

And there is very good reason for this restriction. It encourages 
sincere votes. If the voter doesn't want to risk it, the voter is 
perfectly free and it does no harm for the voter to vote Approval style.

Ranked voting *forces* a Hobson's choice. It works reasonable well if 
your preference strengths are more or less equal. But there are other 
configurations where it doesn't work well at all. The pizza election. 
It can make, sometimes a terrible choice. If it can make a terrible 
choice *when people vote sincerely,* why would we think it would make 
better choices in public elections?

Range makes it *possible* that people can vote fully sincerely *and* 
the method will make the best choice. If they vote sincerely, it 
will. What people point to is that some voters can amplify their 
outcome by voting Approval style. So? They will do so if that is what 
they want. As I've written many times, and there is actually a Range 
Voting page where Warren picked up one of these arguments, there is 
no basis for considering such an approval vote to be insincere unless 
we simply define it as such. Why should we assume that people would 
vote other than what they actually feel. If they feel so strongly 
that the election *must* come from this set, and *not* from that set, 
they have an obvious vote: Yes for the first and No for the second, 
i.e., max and min. The fact that they have some internal preferences 
apparently did not make a difference to them, *these preferences were 
not strong enough for them to vote them as we think "sincere.'*

What we do is to make up some preference scale for these voters and 
then assume that they will act contrary to it. What we've done is to 
set up a distorted preference scale, not their real one. Their real 
one we know from how they vote!

"Why did you rate Nader 100% and Gore and Bush 0%?"

"Well, I thought that there really was no difference between them."

"Sure, Gore is a little better, but it was more important to make a statement."

VOTES ARE NOT NECESSARILY ABOUT THE CANDIDATES. THEY ARE ACTIONS.

They have effects, and the voters know that. They vote to have an 
effect, an effect they want.

So all this pucky about not being able to measure sincere preferences 
is a red herring.

We "measure" them by asking voters. They know how we will use the 
information, and *they* -- not we -- are in charge. We are just serving them.

In the end, what we are measuring are votes. By giving everyone N 
votes, in Range N, we are allowing them some flexibility. We would 
allow more if we could. We'd allow them to ratify the election, which 
in one fell swoop would make the whole thing not only Condorcet 
Compliant, Majority Criterion compliant.

Short of that, we'd hold a runoff whenever it was not clear from the 
election results that the winner has majority consent. It's easy to 
make that explicit on the ballot, you can define a Range rating above 
a certain level -- which can be specified by the voter -- as 
signifying explicit consent.

Approval, of course, collapses this. That's all you can do! But 
because it is collapsed, it can go wrong.
> > 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.

Sure. But it usually does. And if you have a method that can do 
better than Condorcet, by definition, it is not Condorcet compliant, 
it "fails" the Criterion.

But in two stages, you can have your Condorcet cake and optimize 
satisfaction as well.

So if those nasty Approval style voters try to take advantage of the 
nice, cooperative, Sincere Voters, if we would ever be so lucky that 
the latter are in the majority, the Sincere Voters would whup their 
faction in the runoff.

Unless they really did have small preference, in which case they 
wouldn't bother.

You get people to vote sincerely by trusting what they say and giving 
it to them!

(In some election contexts, there may be methods for practically 
defining votes a sincere. You could consider an auction a Range Vote 
for the buyer of the object. -- it's a little complicated, but the 
analogy is there. Suppose the property belongs to the public. 
Everyone bids what they think the object is worth, or maybe less, 
maybe they want a deal, and the highest bidder gets the object, and 
the public gets the proceeds. This is a way of saying that the 
highest bidder pays everyone else the value of the object, perhaps 
relieving them, collectively, of some taxes, or funding some project 
in the public interest. Or, to be sure, lining the pockets of some 
grafters but that's a different problem to be dealt with in a 
different way. Now, we would think it silly to think that someone in 
an auction who voted Approval Style was being cunning and the sincere 
bidders were stupid. But some of us think that sincere voters are 
being stupid.... Now, there are contexts where a sincere vote, 
without any consideration of election probabilities, *is*, if not 
stupid, less than optimal and even foolish.)

You have an election between Al Gore, G W Bush, and Osama Bin Laden, 
I'll pick the current Bete Noir, he  deserves the approbation in my 
opinion. If I thought that there was a real risk that Bin Laden would 
win the election, it wasn't just a joke, I would seriously consider, 
in Range, voting max for both Bush and Gore. And I think Bush is pretty bad!

However, I'd really like High Res Range for this, or a preference 
marker, I'd rather vote 100 for Gore and 99 for Bush and 0 for Bin 
Laden. Bin Laden is bad, but not so bad as to force me to rate Bush 
100 in that context, the risk from 1/100 of a vote is very, very 
small. And then I've indicated preference.

Preference can be indicated in smaller elections by a preference 
marker. The ballot can say

Preferred
Accepted
Rejected

The election can be counted in at least three reasonable ways: As 
Approval, in which case Preferred and Accepted don't affect the 
Approval winner, but may have other effects, and among them is a 
preference indication that the majority would make another decision 
if asked. Another reason to have a preference marker is to measure 
the strength of parties, to allocate space on ballots, and to steer 
public campaign funding, which I'm not advocating, but it is a 
reality in some places.

Next, it can be counted as Range, with a specific Approval cutoff. 
It's Range 2.

And it can be counted Condorcet, which errs a little by presuming the 
Preferred/Accepted preference strength to be equal to the 
Accepted/Rejected preference strength, when it is probably less.

If the election is Range, indeed, it is possible that a more 
sophisticated analysis of the votes would not assign ratings of 2, 1, 
0, but might assign ratings of 3, 2, 0. We have not explored this at all.

Remember, what we propose right now is Approval. Simple. Existing 
runoff rules, in some places, would remain in place and make the 
method better. And a small modification, if politically practical -- 
it might be -- would, in my opinion, make it even better. But the 
traditional practice in public elections, when two "candidates" have 
more than a majority approval, is to elect the one with the most Yes 
votes. (This is done with conflicting referenda.)

*Then* we can start to experiment with Range, starting with test 
elections where the ballot is still counted Approval, but has 
additional rating levels that can be used to study public opinion and 
make, however imperfect, judgements about what the public would do in 
real Range elections. And there will be some Range trials, where it 
can be done. There may also be trials of other methods: IRV, Condorcet.


> >> 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.

Sure, we can say that. The vote pattern is actually a Plurality one. 
I didn't bother to pull up a Condorcet Cycle. In other words, it is 
not crucial for this that all truncated as shown. It is possible that 
they all filled out the ranks and the same argument holds. In a 
balanced election with three candidates, Condorcet can choose a 
winner who is really only supported by a small percentage, 
approaching 1/N, the number of candidates.

> > 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.

Because it was small for them. There is no standard for how strong a 
preference must be in order to be "insincere" if not expressed.

How about I say about Range what you just said about Condorcet, how 
does it sit?

The basic rule (in the absence of strategies) in Range is to express 
one's sincere opinions.

It's not quite true. You should probably do, in public elections at 
this time (not in small elections among friends, used for polling 
purposes), what ranked ballots force you to do: rate one max and one 
min, at least. The rest is fine if it is "sincere."

One more caveat about sincerity in Range. A ballot is not testimony, 
but "lying" can be punished by bad results. What is "lying." It is 
acting contrary to what will produce good results! On a Range ballot 
this is never to reverse preferences. Range in that way always 
encourages "sincere" voting. But if the real election, the real 
question you are being asked by the election *in context,* is Shall 
we elect Bush or Gore, then to rate someone else higher than Gore, 
significantly, is to waste one's vote. Those other ratings aren't 
going to mean beans, it is as if someone went in and erased them, 
leaving the ballot with only your rating for Bush and Gore. If it is 
not the full range left, then you are saying to the *real* method 
that you don't fully care which of them gets elected. If that's real, 
fine. If it is not, your vote was foolish, even though you might have 
thought it "sincere."

This is one reason why I would avoid putting instructions on the 
ballot that tell voters a meaning they should put on their vote. 
Voting for a candidate does not mean that you "approve" of the 
candidate. In an example I gave earlier, I wrote "Accepted" not 
"Approved," and I'm still not happy with even that. But the context 
was that this vote would actually be used as an indicator that you 
accepted the result.

And starting out with maximizing elections so that the winner is the 
one most accepted is an excellent start. Some people posit it as the 
goal itself! I don't think it's that simple.

>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.

Of course. It shows the ranks, unless they are trivial, if the Range 
resolution is sufficient.

So if we did get condorcet somewhere, I'd be pushing for some test 
situations where Range ballots were used.

>Note that if there will be a runoff between the Condorcet winner and
>the Range winner voters may become very strategic.

I think the reverse.

>  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.

Preference cycles, of course, don't occur in Range, only in 
Condorcet. Creating them by reversing preference in Range could 
backfire. And if you aren't reversing preference, you aren't voting 
strategically.

I don't find the scenario believable without a detailed analysis. It 
is far easier said than done.

>This will of course make the ratings more insincere.

In a direction likely to harm those who are voting this way.

>  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.

You have difficulty with that? I find it easy. If I have a preference 
at all, I would vote B,C 1,0, in a pure Range 100 election. The cost 
of indicating the preference is tiny, but for the preference winner, 
it is important. But that's all you need to do to preserve preference 
order. The cost in the Range election is trivial. That's why I say 
that with sufficient resolution, you don't need preference markers.

What's hard about that? The risk that your 1/100 of a vote would be 
the deciding vote in the election? Even if everyone like you voted in 
the same way, well, the chance that your collective accumulated vote 
cents would turn the election against A would be trivial.

Frankly, to understand how to vote in this situation (A is the best, 
B and C are both truly awful, but B is preferred), the only situation 
where I'd need to know the election probabilities is if I knew that B 
and C were the likely pairwise contest at the end, period. A is not 
going to win the Range election, period. In which case I'd vote 
100,x,0, where x would reflect my true preference strengths, 
reconsidered, and might be as high as 99. That is, I want to give as 
much strength as possible to B over C, but to preserve my preference for A.

Range and Condorcet strategy are different, but one principle 
remains, predicting the pairwise contests, and any runners up that are close.


> >
> > 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).

However, the principle is simple. Nominate the Range winner. See if 
anyone beats this candidate pairwise. If so, nominate the Pairwise 
winner and hold a runoff.

That two beat the Range winner is extremely unlikely.

Approval strategy would be suboptimal, because you would want to 
preserve the edge for your favorite. That is, this would encourage 
voters to show true preferences in Range. At least a little.