[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

On 15.01.2022 21:50, Daniel Carrera wrote:
> On Sat, Jan 15, 2022 at 8:41 AM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
>>     The setting may be a bit misleading: in the game that the strategy's
>>     being calculated on, there's first an "honest" round, and then factions
>>     who prefer someone else to the winner get to try to make that
>>     someone win.
> 
>>     In particular, there's no hidden information. In a real election, voters
>>     who prefer some Y to X might not know that Y is the candidate they
>>    should be compromising for, and that e.g. trying to compromise for Z
>>     instead would backfire. So adjusting lower ranks may still be useful in
>>     such a situation, or when the voters are aiming for destructive strategy
>>     ("anyone but T") rather than constructive.
> 
> 
> It is also worth noting that while real elections don't have perfect
> information, they generally do have some information. Most elections are
> repeats of previous elections. Candidates change, but party platforms
> and political affiliations don't as much. It would actually be
> interesting to rethink the "elections" and "candidates" from the
> simulation as instead representing relatively fixed voters and parties.
> We can grab (electorate,parties) where there was a successful strategy,
> and have it repeat the election over and over again, each time allowing
> coalitions to shift their votes, until we reach a Nash equilibrium. I'm
> not exactly sure what I would do with that information though.

Yeah, I'm not sure either. What we'd want to have is a system where the
honest winner is the equilibrium winner as often as possible, although
Gibbard shows that no method is strategy-proof except combinations of
duple (random pair) and random ballot.

I've at times thought that a more realistic approach would be to use
evolutionary stable strategies, e.g. suppose everybody is honest, then
some small faction defecting can't grow in power to the point where
everybody feels the need to vote tactically. But that's even harder to
model, and some societies are used to tactical voting at the start (e.g.
US Plurality elections), and might thus not fit that very well.

> On a mostly unrelated note, I just ran Smith//IRV. Unsurprisingly, it's
> similar to Benham, but there is more room for the JGA strategy:
> 
> - N = 4, V = 99, C = 5
> - Smith//IRV
> - 4.7% of elections have successful strategies
> - 94% of successful strategies are the trivial one
> - The remaining strategies are split 38% "reverse" and 62% "JGA".

94% vs 98% is not that much of a difference, but any little bit helps
(as long as it's not too much at the expense of some other desirable
properties of the method). Increasing the need for complex strategy is
also good, of course, because it's easier to imagine trivial or reverse
than some tailor-made strategy.

Now I'm wondering if the strategically resistant methods mainly increase
their resistance by making it impossible for trivial strategy to work in
cases where it would otherwise work. From my experimentation, I've found
out that reversal symmetry usually makes for a susceptible method, and
that rev. sym. and Condorcet together are incompatible with dominant
mutual third burial resistance.

Perhaps it'd be easier to reason about these implications based on the
trivial strategy. Something like: suppose you vote X>...>Y. If there is
a benefit to voting X first, this must also weaken Y's position, because
with the reversed ballots, Y would be helped by this upranking. (That's
only for my stronger sense of reversal symmetry, though.)

I'd have to think more about it, but I think trying to reason about what
kind of properties reduce the effectiveness of trivial strategy could be
a good approach.

>>     As an argument in favor of Range, Warren sketches a scenario where the
>>     frontrunners are X and Y and everybody either votes X>...>Y or Y>...>X.
>>     As a consequence of the majority criterion, either X or Y wins; and then
>>     he says that this probably will lead to two-party domination because the
>>     strategy is self-stabilizing . The results from the strategy
>>     calculations could be used to back up that argument.
> 
> 
> I'm not sure I understand how this is an argument in favor of Range. The
> JGA paper doesn't include Range, but it includes Approval and Approval
> is one of the easiest to manipulate systems. I would guess that Range
> would be similar. Warren's scenario seems to me like a likely end result
> of the sort of repeat elections leading to a Nash equilibrium that I
> suggested earlier. If we make the simplifying assumption that every
> election that can be manipulated is an electorate that will one day end
> up in a two-party system, it would follow that the systems that are
> hardest to manipulate are the ones most likely to avoid going down that
> path.

He has a few arguments that generally boil down to "if everybody goes on
a burial/compromising spree, then ranked voting does badly but Range
does not". I think his argument in this particular case is that if
voters are all X>...>Y or Y>...X, a common consensus candidate might
still win in Range (e.g. 52 voters X: 10, A: 9, Y: 0, 49 voters: Y: 10,
A: 9, X: 0, then A wins). So the idea is that the voters, used to two
party rules, don't want to risk honesty and instead vote the lesser evil
top and the greater evil bottom all the time, after which the majority
criterion does the rest.

Similar reasoning can be found in https://rangevoting.org/WVmore.html
which seems to argue that DH3 is a problem even for Condorcet methods
that pass DMTBR (like Smith//IRV, Benham, etc):

> But we admit some thinking about cycles was involved, in a sense, in
> the decision by the A- and B-voters to use this strategy (which was
> intended to create a cycle to prevent C from winning and thus cause A or
> B to win). However, we contend many A- and B-voters would have done that
> even without ever having heard of Condorcet cycles, since it is a
> natural attempt to most-hurt their candidates' perceived major rivals. 

In any case, as you say, strategy-resistant methods like the Smith-IRV
hybrids will reduce the chance that strategy works, and so would give
third parties some more room in which to grow.

It would be interesting to do a test with Range; I imagine that it would
be very susceptible to strategy, similar to Approval. And I would also
imagine that STAR would do considerably better.

-km