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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Tue Jun 25 10:38:03 PDT 2013

Benjamin Grant dove in here with some knee-jerk reactions to Approval 
and Score vs. Plurality. Those reactions are not uncommon.

However, what I saw in these exchanges was a collapse of an 
interpretation, based on imagined models of voter behavior that are 
common, but likely very incomplete, with fact.

Let's back up. The advocacy of approval voting became a consensus 
position among students of voting systems because it is an extremely 
simple tweak on Plurality. It is simply an implementation of the 
slogan Count All the Votes.

That has some expected effects, but this is not necessarily the ideal 
voting system. It will, however, very likely, produce some benefits, 
immediately. That is, supporters of minor parties will be able to 
see, in vote totals, a decent indication of real preference. We can 
predict this if approval is adopted:

1. Some increase in the number of minor parties.
2. A reduction of the spoiler effect.
3. A reduction in spoiled ballots.
4. Some increase in majority election results.
5. Better knowledge of true support for minor parties.

Approval has an obvious defect, which is the inability to express 
first preference. That defect must be considered in real systems, 
especially partisan elections, where, currently, a vote counts toward 
maintaining ballot position for a party. That value of a vote was 
completely ignored by Benjamin, he seems to think that voters are 
only considering the current election.

So with raw Approval, something would have to be done with regard to 
ballot position. The only solution I see that is adequately simple is 
to divide the vote, i.e, if a voter has approved candidates from two 
parties, the vote would be split fractionally. Other solutions could 
include a separate vote for a party, vote for one, or if it's 
approval on that section of the ballot, *then* if the voter votes for 
more than one party, the vote would be divided.

But if one is going to go to that complexity, there is then a better 
solution, Bucklin. Instant Runoff Approval. There are many Bucklin 
systems, I won't go into detail here, but the point is that true 
first preference may be expressed, as with IRV, but without the IRV 

Many voters will continue to bullet vote, and if one truly supports a 
frontrunner, that is a totally sensible vote. Practically by 
definition, then, until and unless elections become complex, we can 
expect low usage of the right to add additional votes. From various 
histories, it looks like it could be something like 10%. But 10% is 
easily enough to whack the spoiler effect!

It is correctly understood that Approval has some difficulty when a 
third party candidate rises to parity, and could win. That is where 
the ability to rank approvals can come in. Still, as has been pointed 
out, *we don't know how Approval will behave under those 
circumstances.* The most likely symptom of such a situation, as it 
approaches, would be either majority failure or multiple majorities, 
with "multiple majority failure" being relatively harmless.

It is beginning to look like the most likely implementations of 
approval will be, at first, under runoff systems, or for open 
primaries. However, we have recommended Count All the Votes as a 
principle that can be applied with any voting system. It would make 
IRV perform better, for starters. Why are multiple approvals at an 
IRV rank considered spoiled votes? Why not simply canvass them? Doing 
so would actually allow voters to vote approval style, under IRV. It 
would give those Burlington Republicans an additional choice.

But they would surely prefer Bucklin, which would still allow them to 
express their first preference. *Bucklin worked*, we know that from 
the history.

Now, another imagination from Benjamin is that Range Voting would 
devolve to Approval. He bases this on a belief that any knowledgeable 
voter would vote Approval style, i.e, would either max-rate or 
min-rate candidates.

That pushes a conflict button here, because there are a lot of 
students of voting systems who think this. However, the claim that 
this is game-theory optimal is simply false, neglecting that voters 
have other values than simply generating an individual maximum, based 
only on the effect on a particular election. In fact, from a more 
careful game-theoretical analysis, which I did for a limited case -- 
all these claims of "game theory" have been hot air, for the most 
part -- I showed that the voter could vote approval style *or* cast 
an intermediate vote, and the expected outcome was the same. Further, 
relatively sincere expression is a value of its own for voters. If 
there are two frontrunners, game theory indicates voting min for one 
and max for the other, but that is silent on how one votes for other 
candidates, and if the system allows an expression of preference at a 
minimal weight, there can be other values that would indicate even 
some deviation from the "max/min" rule.

The game theory argument only applies, at best, to front-runners.

I.e., suppose I'm a Nader voter. I might rate Nader 100, Gore 99, and 
Bush 0. That preserves my preference indication (and could be 
important, then, for giving the Green Party ballot position in future 
elections), and the cost in voting power in "defeating Bush" is 
trivial, 1/100 of a vote. If it's Range 9, it would be 1/9 vote, 
still quite small. I'd vote this way (if I were in that position) and 
I'd tell those people who claim that's stupid that they can shove it.

It's highly likely from experience that at least many voters will 
vote intermediate votes, and a remarkable finding of my own study of 
the game theory of this was that the very availability of 
"intermediate votes," as long as *one voter uses them in each race,* 
was a slight overall improvement in social utility from allowing the 
intermediate votes. I think it's because it dithers the vote.

No, Range and Approval are *different* from Plurality. *How 
different* is the issue. The failure mode for Approval requires 
three-party parity; that's addressed by using a ranked Approval 
system like Bucklin. Or Range Voting with sufficient resolution.

Other considerations lead to an understanding that repeated elections 
are needed for full and broad optimization; requiring that decisions 
always be made with a single ballot is a constriction that guarantees 
results that are at least occasionally poor.

The study of repeated elections has been massively deficient, almost 
all consideration has been of the very primitive vote-for-one top-two 
runoff. The paucity of consideration is particularly remarkable 
because the voting system in widest usage, in the U.S., once we look 
at non-governmental organizations, is "repeated election until an 
explicit majority is found." No eliminations.

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