[EM] Strategy-proof vs Monotone

[Kevin Venzke]

Hi Daniel,

Le mercredi 19 janvier 2022, 01:10:59 UTC−6, Daniel Carrera <dcarrera at gmail.com> a écrit : 
> So recently I've been posting a lot about using simulations to estimate which
> voting systems are most vulnerable or resistant to strategy. That was certainly
> interesting. But as Colin pointed out, strategy resistance is not the only goal.
> One issue that keeps coming to mind is that, I think..., all the Condorcet-IRV
> systems are non-motone. Am I right about that? I think all (most?) runoff-based
> methods non-monotone.

Yes, because if you want monotonicity you have to take a lot of care with the
effect of changes in a vote, so that it always works out OK. But runoff methods
are "messy." With IRV this is the price paid for not regarding voters' lower
preferences until the higher ones become unusable.

A finding of Woodall is that a method lacking both burial strategy and
truncation strategy (as IRV and FPP), which also elects from a "mutual majority"
or (similarly) satisfies "Clone-Winner" (as IRV does), can't be monotone.

> So I guess I have two questions:
> 
> 1) How important do you think monotonicity is? I'm not comfortable with the idea
> that you can harm a candidate by ranking him higher, but I would say the same
> thing about failing the participation criterion yet all Condorcet methods fail
> (for reasons I still don't fully understand).

I agree with you that failing participation ought to be considered bad. But it's
extremely limiting to insist on this. The only methods that satisfy
participation are simply adding up points from new ballots, without doing any
fancy math with the totals. The most exotic methods here are Woodall's DAC and
DSC, which sum points for each possible set of candidates in the top positions
of a ballot, and then run down the list doing set intersection.

I'm willing to look past monotonicity failures in order to explore other types
of methods. The failures are unsightly. But often they don't create strategies
that voters could actually exploit. And I think in some cases the unfairness of
monotonicity failures isn't obvious at first glance, which might (I'm not sure)
make it more acceptable.

Also, methods can vary in how egregiously or how often they can violate
monotonicity. One can design methods much worse than IRV here, although I guess
that may not be much consolation.

> 2) Does anyone know a different class of Condorcet systems that are also
> resilient to strategy?

I think it depends what you mean. A lot of studies seem to assume all the
ballots must be complete orderings. In that setting, I think you must use a
method roughly like Condorcet//IRV because otherwise I (speaking personally as
a voter) will feel like I'm being explicitly asked to consider flipping some
orderings around in attempt to avoid helping the candidates that I believe I'm
trying to defeat.

At other times we have sometimes focused on resilience to burial strategy
specifically, not in the sense that the burial incentive isn't actually there,
but that due to certain expectations of truncation on the part of other voters,
voters may consider a burial strategy too risky, and truncate instead.

This is particularly expected when a faction supporting one of two frontrunners
would have to base a burial strategy on the assumption that their candidate
would receive some support from voters supporting the candidate's main rival.
If they don't get this support then they risk electing the candidate they used
for the burial.

To take this stance, you have to understand some truncation as benign or at
least inevitable. I also prefer this stance because the reduced burial incentive
of a method like Condorcet//IRV seems to translate to higher compromise
incentive, which I find unsightly, as it seems to undermine a major argument for
bothering with new methods in the first place.

Kevin