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

Benjamin Grant panjakrejn at gmail.com
Tue Jun 25 08:31:14 PDT 2013

On Tue, Jun 25, 2013 at 5:44 AM, Kristofer Munsterhjelm <
km_elmet at lavabit.com> wrote:

> On 06/25/2013 12:53 AM, Benjamin Grant wrote:
>> 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".

OK, I cannot argue with that.  Once Abe has given his full support to Gore
(to stop Bush), it doesn't harm his desire to stop Bush to also score Nader
at 100. That is simply true.

However, while it doesn't help Bush, I would argue that it won't help Nader
defeat Gore either - I mean, the whole reason this Nader supported is top
scoring Gore in the first place is because it is well known that Gore has a
much better chance (perhaps the only chance) at beating Bush. In such a
situation, giving both Gore and Nader the same number of votes is not going
to change the fact that Gore is stronger than Nader. So it seems irrelevant
whether or not he votes for Nader in this circumstance.

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.

The thing is, I think I agree with most everybody on the list in that I
think Plurality voting is the absolute *worst*.  My worry is functionally
and in practice, Approval won't ultimately fix what is broken in Plurality
- joke third parties and/or the spoiler effect.

> 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 win.

Again, I can't claim that it's not different - I just feel like for all
practical purposes, despite the options, you wind up getting the same
results in practice. Sure we can get more information out of an election,
and that may not be bad. If after all the votes are in, the average scores
are Gore:5.6 Nader 1.3 and Bush 4.7, that's more information for the people
to receive about how people voted than if the plurality vote was Gore: 51%
Nader: 6% and Bush: 43% - or worse yet (to Abe), Gore:43% Nader: 6% and
Bush: 51%.

So I guess Approval, even in worst case strategic situations has a few

   - People who can't not vote for Nader can still help stop Bush by also
   voting for Gore.
   - People who need to stop Bush and were going to vote Gore no matter
   what can now also vote Nader. It is very unlikely to help him win, but at
   least now the election results more accurately reflect Nader's true base of
   support, which could be good info to have.

The only downside is seeing Nader's support rise can lead to people
abandoning Gore to vote Nader, thinking optimistically that they can have
their cake and eat it too. And once Nader supporters get burned by electing
Bush through not supporting Gore, they won't make that mistake again.

However, here's a thought out of left field that simply did not occur to me
before: What if Bush voters, seeing that all the Nader folks are also
support Gore, and possibly seeing that Bush is simply likely to not win,
Approve Bush and Nader, reasoning that if Bush isn't going to win, they
would prefer Nader over Gore? (That may be unrealistic, but I *can* imagine
a third party candidate that would be more centrist and more palatable to
Conservatives than Gore.)

Maybe an interesting wrinkle is that if the Conservative first choice looks
unlikely to win, some of those voters may expand and include another pick
as well, one which may not be as bad as the opposing front runner.

That's interesting.

>     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:
> http://zesty.ca/voting/**voteline/ <http://zesty.ca/voting/voteline/>
> http://zesty.ca/voting/sim/
> 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:
> http://bolson.org/voting/
> 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:
> http://munsterhjelm.no/km/**elections/multiwinner_**tradeoffs/<http://munsterhjelm.no/km/elections/multiwinner_tradeoffs/>
> I also made some multiwinner Yee maps, way back:
> http://munsterhjelm.no/km/**elections/multiwinner_yee/<http://munsterhjelm.no/km/elections/multiwinner_yee/>
OMG, squirelling away THOSE links for consumption - thanks!

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