On 11.6.2011, at 13.30, Kristofer Munsterhjelm wrote:
> Juho Laatu wrote:
>> On 9.6.2011, at 4.54, Kevin Venzke wrote:
>>> Hi Juho,
>>> --- En date de : Mer 8.6.11, Juho Laatu <juho.la...@gmail.com> a
>>> écrit :
>>>> I was busy with other activities for a while but here are some
>>>> comments.
>
>>> I think with C//A it is easier to explain how to find the winner,
>>> and the strategy becomes obvious. No defeat strengths are involved.
>>> MinMax has its strategy too, and this is harder to perceive because
>>> the method rules are harder to understand.
>> If we are taking about simple explanations to regular voters then
>> maybe all the strategy related aspects should be considered
>> not-simple.
>> C//A's counting process is quite simple (to explain) although its
>> counting process has two phases that differ from each others. I don't
>> think e.g. the "elect the candidate that needs least number of
>> additional votes to beat all others" would be more complex.
>
> I think voters could be confused over that where one truncates actually
> matters to the method. That is, the method isn't resolvable if everybody
> votes untruncated and there's a cycle; no single ballot can break the tie
> unless it also breaks the cycle. Further, if only some people truncate, that
> would give power to them.
>
> So yes, the implied double use of the ballot could add more complexity.
> Instead of the complexity being "in front" (seemingly complex method), it's
> "in the back", somewhat akin to the strategy equilibria you can get in the
> seemingly simple plain Approval method.
Cutoffs add information but implicit cutoffs may also decrease information
because of truncation. That could make the winner less ideal than with fully
ranked (also ties possible) votes. All available information may help solving
ties.
>
>> Not necessarily, but that need might pop up. For example in the
>> MinMax(margins) explanation above ("elect the candidate that needs
>> least number of additional votes to beat all others") CW is not
>> mentioned. Some voters might however start wondering in what kind of
>> situations the winner does not win all others. In that case that
>> individual voter might need someone to explain that sometimes there
>> is a CW and sometimes not.
>
> One doesn't have to explain the concept of the CW in least reversal Condorcet
> or Copeland either, nor Tideman or (I think) Schulze.
>
> Even for the Condorcet-IRV hybrid methods, you could slink your way out of
> defining the CW. For instance:
>
> Repeatedly eliminate the Plurality loser among uneliminated candidates until
> one of the remaining candidates beats all the other remaining candidates
> one-on-one.
>
> This "defines" the CW indirectly without mentioning the name CW itself. The
> winner of this method isn't a true CW either, because it's only a CW with
> regards to the uneliminated candidates.
>
> Perhaps you could define Minmax, as an algorithm, like this:
>
> "A candidate beats another if more voters prefer the former to the latter
> than the latter to the former.
>
> If a candidate beats another, the strength of his victory is equal to how
> many voters prefer the former to the latter (WV).
>
> If a candidate beats another, the strength of his victory is equal to the
> number of voters preferring the former to the latter, less the number of
> voters preferring the latter to the former (Margins).
>
> If a candidate is beaten by another, the other candidate's victory is his
> defeat.
>
> Elect the candidate whose worst defeat is least."
>
> (Possible tiebreak: "Break ties by electing the candidate whose second worst
> defeat is the least. Break further ties by third worst, fourth worst, and so
> on. If the tie remains after all defeats have been considered, flip a
> coin/ask the legislature/random voter hierarchy.")
>
> Some methods pass the Condorcet criterion without seeming Condorcet-like at
> all. Nanson and Baldwin, for instance, look like Borda IRV. BTR-IRV always
> keeps the CW in the running and so also elects the CW when there is one. None
> of these examples are monotone, but hey.
>
>> If we take for example a country that uses D'Hondt to allocate seats,
>> only some voters are able to explain how the D'Hondt allocation is
>> actually counted. Most voters vote happily despite of this and have
>> considerable trust on the method.
>> It is possible that the complexity of a method will be used against
>> it in some reform campaigns but maybe that's a different story. This
>> is not really a problem of the regular voters but just a campaign
>> strategy. Defendability in campaigns is a valid separate topic for
>> discussions though.
>
> It might be useful to look at places that have complex methods and find out
> how they got passed. As far as I know, the (quite complex, computer
> calculated) Meek's method is used in certain New Zealand elections. How did
> that happen? How did the voters accept it? Perhaps some of that knowledge can
> be applied to electoral reform elsewhere.
My best guess is that there were some active individuals with marketing skills
too, and a situation where the society wanted some reform. I note that for
example in Finland there is currently a reform plan that has some resemblance
to this pattern. People have long known that the system is not quite ideal.
There were some committees with some wild and some more conservative ideas. The
plan that was already once approved in the parliament includes added complexity
in the form of counting proportionality quite exactly at national level but
still dividing the seats to different districts so that they each get exactly
the correct number of seats, and also to parties and individual candidates
within those districts in a quite accurate way (only plurality based for
candidates though). Now the new parliament should also approve this proposal.
Some politicians may have now woken to the fact that a more proportional system
may not after all be in the interest of the largest parties that won some extra
seats in the old arrangement. Let's see if the politicians will approve the new
and technically more complex system of if the spell of wonderful new ideas has
already faded out. (Well, there is one major problem. The proposal now includes
a national threshold to get any seats at all. That is clearly a non-proportinal
and new feature in the system. But still I think the new system is better than
the old one.)
My point was just that after years and years of living with the old system, now
the time was somehow right (there was e.g. one case where a party leader didn't
get elected although she got lots of votes because she was a candidate in a too
small district), and there were few interested individuals, and the rest of the
politicians accepted those developments although many of them probably have not
studied the properties of the proposal in great detail. One just has to wait
for a few decades and then try to move when the stars are in the correct
position.
>
>>>>> has more obvious burial disincentive (especially if the
>>>>> comparison is to
>>>> margins),
>>>> All Condorcet methods have a burial incentive with some variation
>>>> between different methods. I don't know why margins would be more
>>>> problematic than winning votes.
>>> The theoretical reason is that the offensive and defensive
>>> strategies look exactly the same. It's analogous to Borda. You
>>> cannot tell whether somebody is trying to steal an election or just
>>> cover themselves.
>> I'm living in the hope that strategic voting would not be widely
>> spread in Condorcet methods. If strategic voting (offensive and
>> defensive) becomes the norm, Condorcet methods might well lose their
>> attractiveness. If regular voters have to start thinking about
>> offensive and defensive strategies instead of just indicating their
>> preferences they might get fed up pretty quickly.
>
> I imagine there's a threshold effect. Below a certain point, it doesn't pay
> to strategize so those people who do it soon find out it isn't worth the
> bother and so don't do it. Above this point, low variety coordinated strategy
> works (parties producing how-to-vote cards). Above another point,
> uncoordinated strategy works (heaping clones or nobodies on your opponent in
> Borda, voting for the lesser evil).
I'm interested also in thresholds in the morale of the society. I mean that in
Approval everyone is expected to cast a strategically optimal vote (instead of
marking those candidates that the voter would sincerely approve for the job).
On the other hand in the same society if someone tries to fill and return two
ballot papers, the rest of the society could react strongly and the reputation
of that person could be lost for years. There are thus moral codes that the
society sets. In all societies there are things that you are supposed to do and
things you are not supposed to do (and things where you can decide yourself).
Some things are enforced by the police, some by your fellow citizens.
Condorcet methods are interesting since for example the burial strategy is
quite radical in the sense that it appears that someone tries to take something
that does not belong to him. In some societies people that try to make use of
these features of the method might be considered smarter and more competent in
influencing the society while in some societies such people could be considered
immoral (and they would most certainly not brag about trying to fool the system
to other (decent and non-criminal) members of the society). Also the society
might thus add some more hysteresis to the equation in addition to (or to
strengthen the influence of) the technical properties of the methods.
>
> If your method is below the first point, all's well. If it's between the
> first and second, you may get coordinated strategy, and in that case, the
> game theoretical equilibria matter. Furthermore, the coordination requirement
> may bar smaller parties. If it's above the second, there will be a lot of
> strategy.
>
> Where those points are, though, I don't know. The first point may be lower
> than one thinks, however, because it's enough that strategy of some form
> doesn't work; if small scale coordinated strategy doesn't, parties may not be
> able to or interested in risking costs for a very large project just so they
> can strategize. (It's kind of like law enforcement in this matter -- you
> don't have to catch absolutely every bad guy.)
>
> About the only thing we know from strategies is that Plurality with more than
> two parties is above the second point. Borda is also above the second point
> (e.g. Tim Hull's observation as mentioned on the RangeVoting pages). Approval
> is above the second point, too, but to Approval, that's a feature: one points
> at the equilibria and say "hey, you'll get the sincere CW this way so no
> problem!".
>
> Runoffs seem to be below the first point, though I don't have many sources
> for this. The second round is honest (with reminders to "vote for the crook,
> it's important" if necessary). I don't think I've heard of attempts to
> strategize votes of the first round. Runoffs seem to be robust enough to
> support multiple parties, at least in France.
>
> Hopefully most methods will fall below the first threshold or require such
> coordination that it doesn't matter. There seems to be some anecdotal
> evidence for this with regards to Bucklin; if the Plurality winner could just
> out-strategize the rest, he wouldn't have had to take it to court. STV seems
> to be below it (the threatened parties in New York tried vote management but
> didn't really get it to work), but Schulze's paper might suggest it's at the
> lower end of the "between first and second" domain.
>
> (Perhaps top-two runoff would be the easiest improvement to the US
> presidential election. It's proven, simple, and it seems to support many
> parties.)
Yes, I wonder why there are no such activists. Maybe US people want something
US specific. Top-two runoff is not an ideal method but it has some interesting
properties. It collects so little information that it is not usually possible
to prove that the method failed to elect a true Condorcet winner (or that some
potential winner didn't make it to the second round). IRV collects more
information and therefore you can see when such failures occur. Top-two runoff
also makes it possible for smaller parties to grow and sometimes win the
election, or to have excellent candidates and therefore win the election. It is
for example possible that in a series of elections some small party grows and
grows until it is bigger than one of the (two or more) large parties, and then
wins the second round. Approval for example is likely to have much bigger
problems when a small party grows. Top-two runoff has sometimes chosen "wrong"
candidates to the second round, but in that case the "right" candidate usually
wins, and the surprise was only temporary. I don't think top-two runoff is
ideal but clearly it works and it could be at least a very well working
intermediate step (maybe even too good in the sense that people don't appear to
have any great needs to move forward from it).
>
> The picture for strategic nomination would be similar, but there would only
> be one threshold. Also, in small elections, the two would merge because the
> people can more easily coordinate. For instance, the repeated aye/nay type
> voting in legislatures (which is Condorcet on the face of it) can be
> strategized by crafting proposals that produce Condorcet cycles.
Yes, this is an important area where use of Condorcet should be considered. In
addition to having planned order in the chain of pairwise votes it could be
interesting also to include slightly different versions of the proposal in the
election. I mean that if there is a proposed law, some people (insiders) might
tailor it so that it has some properties that are unwanted to many but so that
the proposal is still acceptable to a a majority or better than the competing
proposal. If we would have a Condorcet election one could include also some
additional versions in the election, and people could decide to approve such a
version of the law where *all* the details are ok. I don't know what would
happen in real life, but in principle a more sophisticated method may allow
voters (MPs) to take more control on how things will go (instead on the smoky
room strategists). Condorcet would be worth a try in legislative and other
everyday work too.
Juho
>
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