[EM] Range Voting "unbeatable"?

[Jameson Quinn]

2009/8/30 Warren Smith <warren.wds at gmail.com>

> >> Warren defines BR in such a way that Range is unbeatable
> >> given sincere votes.
> > Absolutely...
>
> --Sorry: these claims, although stated with the utmost apparent
> confidence by their authors, are utterly false.   Range voting is
> beatable, and has been beaten, with honest voters -- and I was the one
> who did that!


It's a nice result, but it relies completely on the specific probabilities
derived from a perfect knowledge of the underlying voter model. So "utterly
false" is a bit strong language. It would be possible to create voter models
to satisfy any given "reweighting scheme" like the one you used, including
the null-reweighting of vanilla Range. And if you want to talk about
cross-model performance, you need metrics - I suspect that you're right, the
most natural metrics do not favor Range, but a metric could certainly be
constructed to favor Range.


>
> Further, certain systems also beat range voting with *strategic*
> voters, for example
> range+top2runoff system with 2 rounds beats plain range (i.e. has
> lower BR) if there are about 75% or more strategic voters in the mix.


I completely reject your model of strategic voters. It is simply not true
that, if you surveyed all voters their honest opinions of who the two
"frontrunners" are, all of them would agree in 100% of elections. Empirical
evidence suggests otherwise even in plurality systems (sometimes major
parties break down, sometimes voters are honestly deluded); and it is
certainly arguable that this would be even less true in other systems. The
paper you referenced shows that Plurality is especially bad in that it
suffers a "phase transition" with any epsilon of strategic voters (and, by
extension, if the group of strategic voters who believe in any given
candidate is one of the frontrunners is larger than the group for any other
candidate); in the real world, where a non-0 number of voters are
intrinsically honest, you have not shown that your simplistic "two
frontrunners" model for voter strategy is any kind of equilibrium strategy.

I propose (and you have not responded) a different model of strategy.

1) Choose an underlying voter utility model which behaves roughly like
reality. This is an area for research, and my own incomplete ideas don't fit
here, but suffice it to say that the RNEM is not good enough (for instance,
as you point out, it has a majority-top winner with 0 probability, whereas
empirically it's closer to 50%).

2) Create virtual electorates and conduct "polling" in which a sample of the
electorate gives their randomly-truncated ranked preference list.

3) Create (by hand or using genetic programming) and test "strategy
heuristics", by which a given voter can use the polling (and knowledge of
the underlying probabilistic models) to estimate the expected value of
various strategic options, assuming all similar voters use the given
strategy, and assuming no counterstrategy or defensive strategy.

4) Each voter has a strategy threshold - they will use a strategy if the
expected value is above the threshold.

5) Run the election and measure BR

6) For a sample of elections, evaluate whether counterstrategy would be
effective. Hopefully, for most good election systems and strategic
thresholds, this will be a negligible effect.

7) If counterstrategy is not negligible, try to find the
(perfect-information - not poll-based) Nash equilibrium for some simple
cases with the fraction of strategic voters observed in 4 and 5. (This could
be either a degenerate "two frontrunner"-type equilibrium, or some mix of
honesty, strategy, and counterstrategy)

This is a significant amount of work per voting system evaluated, but
Condorcet methods generally would probably have similar results, so two of
them would not be twice the work, while several other systems would be
strategically degenerate (I suspect Range->Approval and
{IRV,Borda}->Plurality for all strategic voters).


>
> Range+top2runoff does beat range if the strategy-fraction is large, but it
> doesn't beat it by much (10-30% regret reduction); meanwhile range
> beats range+top2runoff by a lot more than that if the honesty-fraction
> is large.
>

Again, this is totally dependent on your definition of "strategy".


> So in view of this, at present I still think plain range voting is a
> pretty good choice.
>

I agree. But it is not as great as you depict it. Just as you can make any
Condorcet system behave like Plurality by assuming 2 frontrunners and 100%
strategy, I can make Range behave like "random candidate" by assuming that
candidate X's voters strategically bullet-vote and all other voters vote
honestly. (For infinite numbers of voters in RNEM, you just assign a random
epsilon(k) fraction of bullet voters to each kandidate, and then whichever
one has the highest epsilon(k) wins.) Both assumptions are unrealistic
worst-cases but arguably a significant drain factor on the systems' overall
quality.

Jameson
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