[EM] Quick and Clean Burial Resistant Smith, compromise

[Daniel Carrera]

On Sat, Jan 15, 2022 at 8:41 AM Kristofer Munsterhjelm <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.

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".


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.


However, it may well be that if everybody but one voter is doing so, and
> a third party voter does A>X>...>Y instead of X>...>Y, then X still
> wins; and so on up until enough tird party voters put A first, after
> which A wins. And if the X>Y voters can't all be relied on to put X
> first no matter what, then such weaker strategies may grow until there
> are no longer only two frontrunners.
>
> Dynamic strategy (my response to your response to...) is much harder to
> model than static. But I would expect that methods that resist static
> (one-shot) strategy better would also resist dynamic strategy better.
>

That would be my guess too.


-- 
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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