[EM] C//A

[Kristofer Munsterhjelm]

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.

> 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.

>>>> 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).

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.)

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.