[EM] C//A

[Juho Laatu]

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.laatu at 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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