[EM] Proposed bullet-voting prohibition criterion

[Kristofer Munsterhjelm]

On 01/30/2013 05:30 PM, Peter Gustafsson wrote:
>
> Kristoffer:
>
> Thanks for pointing out those possibilities for how a big party can
> instruct its voters on how to thwart the intent of this proposed
> criterion. Obviously, BVP is not sufficient to ensure the transition
> from a two-party environment to a multiparty environment. What are your
> ideas on how make a stronger set of criteria to that end?

I don't think we can get multipartyism by outlawing duopoly behaivor. 
The life has to come from dynamics brought by other properties of the 
method. It's sort of like that you can't get plants growing in a desert 
by just stating that you're going to plant something at least once a day 
in a desert area; but if you can get an ecosystem going, supported by 
irrigation and such, then it's another matter.

So, for voting methods, I think the "irrigation" comes in form of 
criteria that ensure that the wishes of groups of various forms will be 
respected. This produces a more accurate method; then the translation of 
the people's wishes into a candidate selection is better, and this in 
turn can support multiple parties.

Exactly what kind of criteria you would use would depend on the voter 
population. If the voters are very strategic, strategic resistance 
criteria is important or you get garbage-in garbage-out. If they are 
not, then accurate translation criteria are more important. I don't 
think there is any deductive way to get at how strategic the voters 
would be, and propensity to strategy might also change with time. Thus, 
the best indicator is actual evidence taken from voters actually ranking 
or rating candidates -- and possibly from counterfactual reasoning of 
the form "if there was a lot of strategy going on here, then results 
would be like X, but we know results are Y, so there wasn't".

I think that the evidence shows there's not an undue amount of strategy 
by the voters, while there may be a greater amount of strategy by 
(comparatively more organized) parties. Thus I think that the method 
should deter party strategy and be accurate with respect to voters' 
wishes. (I could go on about the details of this weighing if you're 
interested, but it's a side point to this post)

More concretely, that translates into, for candidate election methods 
(as opposed to PR methods):

- Majority criterion: a majority's wishes on which candidate is elected 
is respected
- Mutual majority criterion: a majority's wishes on which set of 
candidates the winner comes from is respected
- Condorcet criterion: if there's a candidate that would win a runoff 
against every other candidate, ballots unchanged, then that candidate 
should win.
- Smith criterion: if there's a small set of candidates, any of which 
would win a runoff against any candidate outside the set, with ballots 
unchanged, then the winner should come from that set.
- Independence of clones criterion: turning a candidate or party into a 
bunch of identical candidates or parties (that all voters rank next to 
each other) shouldn't alter the outcome.

And then, if I can get further accuracy guarantees, like uncovered set 
("the candidate is elected from a set of candidates that would win if 
everybody strategized and communicated with each other", if I recall 
correctly) or local IIA, then all the better. But I don't yet think 
these are important as such - they are icing on the cake.

Now, it might be that only PR will give us multipartyism and 
single-candidate elections (or single-member district elections) are too 
centralizing to give multipartyism in anything but very large nations 
like India. I don't know if that's the case, as I have no evidence. I do 
know, though, that PR gives multipartyism, so I'm also interested in 
making better proportional representation systems.

For PR methods, there are similar accuracy criteria, like the Droop 
proportionality criterion, which says that if there are n voters and k 
seats, and more than q * n/(k+1) voters rank a certain set of p 
candidates ahead of everybody else (but not necessarily in the same 
order), then the minimum of q and p candidates should be elected to the 
assembly.

(For some time, I thought that the Droop proportionality criterion was 
incompatible with monotonicity, but it seems I've found a method that 
satisfies both. I have no proof of this, though!)

One might also envision a more complex criterion for divisor methods: 
"if everybody votes bloc style" (i.e. only candidates from one party, 
leaving rest unranked), "then the number of seats per party should equal 
that given by the corresponding party list PR method".

The general idea is to distill the people's preferences accurately into 
the outcome - as accurately as you can given the amount of gaming that 
the voters engage in. The better you can do that, the more likely it is 
that you'll get multipartyism -- but only if the voters want it. Malta 
uses STV which satisfies the Droop proportionality criterion, but it 
still is two-party-governed.

> As to your note about range voting: If the rule allows a vote in
> which  one candidate gets 99 points, another 1 point, and all others get 0
> points - then that is so close to bullet voting so that it should for
> all intents and purposes be considered such. I want the voting system to
> be designed so that valid votes are significantly different from a
> bullet vote.

You have a point, but that introduces a Sorites problem. We know what is 
essentially bullet voting in range (99, 1, 0), and we know what 
definitely isn't (99, 27, 0); but where do we draw the line? If we 
decide upon (99, 10, 0), then why is (99, 9, 0) bullet-voting? So 
perhaps it's better to just consider the BVP to not apply to rated 
methods. The spirit of the BVP would seem to be to not accept ballots 
that display preference for only one party, but if preference is 
absolute, it's very hard to detect when it's only for one party.