[EM] Why the concept of "sincere" votes in Range is flawed.

[Abd ul-Rahman Lomax]

At 01:40 PM 1/16/2009, Jobst Heitzig wrote:
>Dear folks,
>
>I haven't followed this long thread, so perhaps this has been 
>mentioned before. If so, sorry...
>
>Abd ul-Rahman Lomax wrote:
>>Because the concept was developed to apply to methods using a 
>>preference list, whether explicit on the ballot or presumed to 
>>exist in the mind of the voter, a strategic vote was one which 
>>reversed preference, simple. But with Approval and Range, it is 
>>possible to vote equal preference. Is that insincere if the voter 
>>has a preference? The critics of Range and Approval have claimed 
>>so, and thus they can claim that Range and Approval are "vulnerable 
>>to strategic voting."
>
>In my view, the main question in the whole strategy-proofness debate 
>should be this:
>
>To determine how I should vote, is that quite complicated or does it 
>depend on what I think how others will vote?
>
>Or is my optimal way of voting both sufficiently easy to determine 
>from my preferences and independent of the other voters?

There is a very serious error incorporated here, which is that human 
beings discount improbable outcomes in determining preference 
strengths. Suppose it's Range Voting. Can I Range Vote regardless of 
the probability of success for each candidate? Sure, I could. 
However, my vote will be ineffective, quite likely. To really bring 
this into perspective, consider that any voter may be able to write 
in a candidate. Let's also postulate a ballot where *two* candidates 
can be written in.

So I decide to write in my absolute, total favorite possibility. How 
much better would this candidate be than the best candidate on the 
ballot? And I also write in the worst candidate I can think of. How 
much worse would this candidate be? Now, if I think try to figure out 
my utilities for each candidate, I'm probably going to cluster them 
somewhere near the middle. And thus, *in the real election*, I 
cluster them near the middle.

But what do voters actually do? The consider the realistic candidate 
set, and normalize their probabilities to that set.

In most elections the realistic candidate set is only two candidates. 
Sometimes it might be three, very rarely is it more than that. So the 
voter will sensibly normalize to only two candidates, usually. But 
this is strategic voting.

Is "strategic voting" -- this kind -- complicated? No. It's actually 
*instinctive.* Most people won't even think about canddiates not on 
the ballot, and they won't sweat over minor candidates, unless they 
prefer them, which is, by definition, not common.

It's true: preference order is relatively easy to determine *if equal 
preferences are allowed.* In Range voting, I'd personally start with 
preference order. Borda Count institutionalizes this; Borda Count 
with equal ranking allowed is easier to vote than pure Borda Count, 
generally, because the voter can simply determine preferences and 
then, when determining a preference is difficult, equal rank. The 
only "problem" is where to put the empty rank that's created.

But this kind of Borda Count *is* Range Voting.

The idea that it's difficult to vote Range is based on the idea that 
voters must somehow figure out a complicated strategy that depends on 
other voters. No, they don't need to. They can *somewhat* increase 
the power of their vote if they simply rank, first, the likely candidates.

This is what we do all the time with choices. Thinking only of likely 
possibilities: Favorite: top rank. Worst: bottom rank. The rest 
either in between somewhere or equal ranked with one of the first two.


>If the latter is the case, the method deserves to be called 
>"strategy-free". The whole thing has nothing to do with "sincerity". 
>Refering to "sincerity", that concept in itself being difficult to 
>define even for methods as simple as Plurality, complicates the 
>strategy discussion unnecessarily.

Sure. But what I'm pointing out is that "strategy-free" is actually 
undesirable. Sure, if we could extract a complete set of absolute 
utilities from each voter, we would have a strategy-free method, and 
a desirable one, but a very cumbersome and difficult method to 
implement. Short of that, attempting to create strategy-free methods 
forces us into the arms of what is worse: the neglect of preference 
strength. And we still end up with vulnerability to *insincere* 
strategy, with the only argument for these methods, in this area, 
being that they are more difficult to follow. Which, of course, 
ignores the possibility of voter coordination, whcih could use very 
complex strategy.

>Applied to Approval and Range Voting, this clearly renders them "not 
>strategy-proof", since optimal strategy does heavily depend on what 
>I think others will do. Random Ballot, on the other hand, is clearly 
>"strategy-free" since my optimal strategy is always to tick my favourite.

Right. Now, how smart is that as a voting method? It produces really 
good results *on average*, but the range of variation is probably unacceptable.

*Optimal* strategy depends on what you think others will do. Sure. 
But a simple sincere vote in Range is actually almost as powerful, 
the difference isn't large, and many voters will vote that way and 
have little or no reason to regret it. Others will bullet vote, and 
only if they bullet vote for a minor candidate might they regret it. 
So, *in practice,* in substance, and for most voters, Approval and 
Range Voting are strategy free. And that's why Brams could have made 
his claims about Approval and why they were reasonable. In order to 
be able to criticize Approval on its vulnerability to strategy, 
critics had to redefine strategic voting in the way that Jobst now presents it.

It used to mean preference reversal.