[EM] Score Voting and Approval Voting not practically substantially different from Plurality?

Kristofer Munsterhjelm km_elmet at lavabit.com
Tue Jun 25 02:44:46 PDT 2013

On 06/25/2013 12:53 AM, Benjamin Grant wrote:
> On Mon, Jun 24, 2013 at 6:06 PM, Kristofer Munsterhjelm
> <km_elmet at lavabit.com <mailto:km_elmet at lavabit.com>> wrote:

>     Also, Range could possibly give different results than Approval
>     voting. Consider an election where 99% of the voters are strategic.
>     The vote comes out to a tie between Nader and Gore, according to
>     these 99%. Then the remaining 1%, voting sincerely, vote something
>     like [Nader: 90%, Gore: 70%, Bush: 10%] (strategic would be [Nader:
>     100%, Gore: 100%, Bush: 0%]). Then those votes break the tie and
>     Nader wins.
>     For reasons like this, a mix of strategic and honest voters give
>     better results than just having strategic ones.
> Of course, there are (in the circumstance where Gore is the better
> chance to beat Bush than Nader) likely more Gore:100 Nader:0 Bush) votes
> than Nader: 90 Gore:70 Bush 10 ones.
> In fact, given that we *are* talking about an election with two strong
> front running candidates and one "spoiler" weaker one, isn't it *far*
> more likely that Gore is far in front of Nader and the only real unknown
> is if Gore will beat Bush or not? Which leads right back to the entire
> scenario of issues I began with.
> The thing is, whenever we have more than two parties running, I think we
> will always have weaker "spoiler" parties that cannot really win, but
> that can, if the system allows or encourages people to vote against
> their best interest, cause people to get a much lower ranked choice,
> possibly their least preferred choice - this is my whole concern.

But here's a thing also to note. Nader voters are never worse off by 
voting [Nader: 100, Gore: 100, Bush: 0] than by voting [Nader: 0, Gore: 
100, Bush: 0]. Because of this, a simple Approval strategy goes: "Vote 
for the frontrunner if you prefer him to the second-place candidate. 
Then vote for everybody you like more than the candidate you approved in 
the first step".

>     Stage two and the transition to three is the tricky part. In rounds
>     of repeated polling, the voters start off cautious (approving both
>     Nader and Gore). Then they see that Nader has approval close to
>     Gore's level, so some start approving of Nader alone. This then
>     reinforces the perception that Nader is winning, so more voters
>     approve of Nader alone. And so it goes until Nader is slightly ahead
>     of Gore and wins.
> Aha! But what if what is likely happens in stage two: People get ahead
> of themselves and give their full support to Nader and less support to
> Gore *before* Nader is strong enough to beat Bush? Then Bush wins, both
> the Nader and Gore voters freak out, and now Nader people go back to
> voting Gore with full support, because now they've been burned!
> The only way to avoid this, I *think*, is with a system in which
> expressing a preference of A over B doesn't let C win - and such a
> system may well have worse flaws, possibly.

Yep. That's a very definite risk, and one of the reasons I don't think 
Approval is a good method "in a vacuum". I'd support Approval as a 
compromise more because it gives a lot of benefit for a very small tweak 
to Plurality, than that it is good in itself: a value/cost consideration 
rather than a raw value consideration.

But you're right, the problem there is very real (unless somehow the 
voters only think of candidates as "people I can accept" and "people I 
definitely don't want to see in office"). And the burn, as you put it, 
could not just harm Nader, but it could harm Approval itself -- just 
like I've argued that the weird way IRV acts can backfire.

So, for rated methods, I suggest Majority Judgement. It's more resistant 
to strategy, the ballots are set up so as to encourage comparisons to a 
common standard (the grades) rather than comparisons between candidates, 
and the method passes IIA. There's also experimental data from its use 
in France. The proposers found out that IIA is too weak when the voters 
compare candidates to each other, because the addition or removal of 
candidates may lead the voters to change what they put on the ballots. 
Thus, they emphasize the importance of having the voter evaluate the 
candidates against a common standard rather than against each other: 
because otherwise, IIA doesn't amount to much.

For ranked methods, I support Condorcet methods, particularly the 
advanced ones like Ranked Pairs and Schulze.

>     So, the way I see it: Approval is very simple on the front end. It's
>     just "count all the votes". Back end is a completely different
>     matter, as you see above. I think Approval pushes a lot of the
>     oddities of voting into the "back-end" - the space in which the
>     elections happen, as it were. The method itself appears to be very
>     good (pass FBC, etc), but that's because the calculations happen in
>     the minds of the voters before they submit their ballots and the
>     criterion failures are therefore "hidden". If one were to make a
>     computerized system that took preferences as inputs and then
>     directly produced the output that the voters would be thought to
>     reach through repeated polling, that system would probably fail
>     quite a number of criteria.
>     But it is better than Plurality. It is nowhere as complex as IRV, it
>     is just "count all the votes". As a compromise, it's better than not
>     reaching any compromise at all.
> Well, to be fair, just about anything is better than plurality. However,
> what I meant is that functionally Approval (when each voter acts to
> their best (or least bad) outcome) seems not that different from
> Plurality Voting. We still top vote the front runner that has the best
> chance to defeat our abhorred candidate. If we have a candidate we
> prefer more than the palatable front runner, we can top vote him too,
> but that won't help Nader beat Gore. It seems irreconcilable in this
> context.

In Approval, you can choose between helping Nader beat Gore, or helping 
{Nader, Gore} beat Bush. In Plurality, you can choose between helping 
Nader beat Gore or helping Gore beat Bush. The whole dynamic of the 
readjustment in stage 2 depends on the voters being able to tell others, 
through the poll results, that they prefer *both* Nader and Gore to Bush.

As such, Approval is better than Plurality. If the tricky part between 
stages two and three go off well, then Nader wins. In contrast, in 
Plurality, there's no way to get to stage two itself because signaling 
that you like Nader carries such a high cost of potentially making Bush 

>     Still, there are results that are valid within certain domains. For
>     instance, Black's single-peakedness theorem says that if all voters
>     have preference functions that are highest at some point on a line
>     and decrease from there (without increasing again), and the voters
>     rank the candidates in order of preference, then any Condorcet
>     method picks the candidate closest to the median voter. Also, IIA
>     holds in such a situation because there are never any Condorcet cycles.
> Yup, that's where I will begin making charts! ;)  (Seriously.)
> I just have to find the time and focus to bring my endeavor with this to
> that level.

You might be interested in Ka-Ping Yee's work. I've linked to some of 
it, but here it is again, along with some other stuff:


Also, there's Brian Olson's page with some more Yee diagrams as well as 
some graphs of the performance of various methods as the number of 
candidates increase:


Myself, I originally investigated the tradeoff between representation 
accuracy and majoritarian appeal of assemblies elected by various PR 
methods, and I made something like this:


I also made some multiwinner Yee maps, way back:


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