[EM] Forced strictly-dishonest strategy is common in Schulze-beatpaths voting

[Kristofer Munsterhjelm]

Dan Bishop wrote:
> You can't just assume that people would vote strategically in Schulze 
> elections because they vote strategically in Plurality elections.

The question of what strategy will be used and to what extent is a quite 
difficult one. On one hand, individually speaking, voting is not "worth 
it", so that weakens utilitarian arguments. On the other hand, we do 
know that some strategy happens: vote-splitting compensation (best of 
two evils) in Plurality, and extreme teaming in Borda.

Generally speaking, I think we can say this: simple strategy will be 
used by a lot of people. Defensive strategy will be used more often than 
offensive strategy, because even the "honest" people may argue that 
"previous offensive strategy has backed them into a corner".

Sophisticated strategy will be used, if by anyone, by teams or groups 
(like parties), because these command a block of voters, and thus voting 
a certain way can definitely be "worth it". Therefore, one can apply 
utilitarian/rational analysis to these teams with greater success than 
one would to individuals.

What limits sophisticated strategy by the teams? First, there's social 
approval. In a honest society, voters may not want to follow party 
instructions, or society in general may see the use of strategy as 
"cheating". Because we're talking about sophisticated strategy, there's 
no gradual corruption, because a team of significant size would have to 
start strategizing. Call the minimal team size that can pull off 
strategy, x. If social disapproval makes strategy backfire on any 
strategizing group of size greater than y, and y < x, then it forms a 
barrier to using strategy.

Second, there's simple logistics. Schulze gives an example in his STV 
paper, about how the ideal vote management strategy in a certain case 
would have been to have 720 (6!) bailiwicks and assign a particular 
order to each ("Free Riding and Vote Management under Proportional 
Representation by the Single Transferable Vote", section 4.2). However, 
this would clearly be a logistics nightmare.

What does all of that suggest, if I'm right? It is that if we aim to 
deter strategy, a method should have as complex strategy as possible; 
first, because that keeps "simple strategy" (tactical voting) from being 
used, and second, because it makes vote management as hard as possible 
to execute, both in terms of minimum effective group size and of 
logistics required to coordinate the strategizing effort.

Perhaps some form of DSV would work? Declared strategy voting would make 
a computer strategize for the voters "more effectively than the voters 
themselves" can. The idea would be that the various sorts of strategy 
cancel out and leaves a somewhat fair result, although perhaps of less 
quality than if there were no strategy in the first place. (At this 
point it may be tempting to let voters decide whether or not strategy is 
to be used, so that the method theoretically reduces to the no-DSV 
version if everybody is honest - but I don't think it'll be obvious to 
voters when to let the computer strategize for them, and when not to.)

The problem with DSV is that the all-strategy version may break various 
criteria. Even if the base method is monotone, the "let the computer 
strategize" version might not be, for instance, since strategic power 
isn't evenly distributed.
Practically speaking, DSV might be too complex for the electorate. If 
they can't convince themselves that the computer will strategize better 
than they do, they may try anyway; or they may look at the result with 
suspicion because it's the output of an opaque black box, to them.