[EM] reply to Juho Laatu on range voting

[Juho]

On Dec 18, 2006, at 1:05 , Warren Smith wrote:

>> Juho Laatu:
> Here's my quick characterization [of range voting]:
> - RV is a wonderful method for dominantly non-competitive elections
> and polls
> - RV utility function is very good when compared to most alternative
> methods
> - RV is very vulnerable to strategic voting
> - but strategic voting is indeed simple, just vote as in Approval
> - also the FAVS properties of RV make it a nice and understandable
> tool for the voters
> - in competitive situations where most voters vote in Approval style
> RV may still elect the Condorcet winner with quite good probability
> (but only with probability)
>
> RV is certainly one of my favourite methods for seeking answer to
> question which one of the clouds on the sky is the prettiest
> (assuming that we want an exact result and are not afraid of doing
> some calculations while lying on the grass). But when we move to
> competitive elections in a traditional (typically competitive)
> democratic society RV is not my first choice ... reasons:
> - RV does not support the idea of "one man one vote" very well (well,
> in theory yes, but...)
> => strategic (Approval style ballot) voters may gain multiple times
> the weight of a sincere (Range style ballot) voter
> => radical voters ("the competing candidate is all bad") voters may
> have multiple times the weight of a moderate ("the competing
> candidate is not quite as good") voter
> - if RV becomes in practice Approval, then the RV side is a trap for
> voters (that are competitive but) who don't know that their vote is
> more effective in Approval style
> - RV "rewards" individual voters that vote strategically by giving
> them more power
> - strategic voting is beneficial in practically all situations (not
> just in extreme cases and/or requiring detailed information and/or
> coordination and/or having risks of failing and/or causing damage
> instead of benefit to the voter)
>
> In highly competitive situations one could use Approval (RV 0..1)
> instead of normal RV (=when one doesn't want to recommend the voters
> to use Range style). But if one does so, then one could also consider
> using Condorcet or other corresponding methods that have been
> designed to cope in competitive environments (like Approval does) but
> that are more expressive than Approval.
>
> --REPLY by Warren D Smith:
> First:
> A theorem ( http://rangevoting.org/AppCW.html )
> indicates that range and approval voting both return the honest- 
> voter Condorcet
> winner if all voters act strategically.  Basically, if we are not in
> the "prettiest cloud" but rather in the "I love/hate Nixon"  
> emotional mode,
> then we vote max or min on Nixon.  Assuming all voters do that with
> their threshold placed somewhere between the two candidates they  
> judge as most likely to win,
> (which they do because they are not strategic idiots)
> and assuming one of these two happens to be the honest-voter  
> Condorcet winner, then
> theorem: Range & Approval both will elect the honest-voter  
> Condorcet winner, but meanwhile
> Condorcet methods often will fail to do so.  [Juho Laatu claims  
> misleadingly
> that "RV may still elect the Condorcet winner with quite good  
> probability
> (but only with probability)."  Actually, under these assumptions,  
> the probability is 1.
> Further, Condorcet methods with strategic voters will elect the  
> honest-CW with
> merely a probability strictly below 1.]
>
Ok, you made some additional assumptions (all voters strategic, one  
of uniformly identified top candidates is the Condorcet winner) that  
I didn't make. With some appropriate assumptions RV behaves as  
described.

> Second:
> The claim that "honest" Range Voters can have their votes
> outweighed by large factors by strategic ones, is correct.  However,
> (1) at least their honest
> vote will never actually work against them (e.g. compared to not  
> voting at all) and

Yes but when compared to voting strategically (Approval style) their  
honest vote works against them (=reduces the strength of their vote).

> (2) their honest statement "X is my favorite" in their vote, will  
> never hurt them.
> With every Condorcet method, by theorem, both of those properties  
> are false.
>
Yes, Condorcet methods have some characteristics that are uglier than  
those of RV. This doesn't mean that their overall usefulness/ 
usability would follow the same logic.

> Anyhow such outweighing
> (a) does not matter if strategic and honest voters have the same  
> political distributions,

If this "same political distribution" is caused by clever and  
strategic people having more weight and others having less weight  
that would change the "one man one vote" towards "clever man several  
votes" which I don't find very tempting. And even if we were lucky  
with the statistics already relatively small changes in the balance  
could change the outcome of the election considerably.

I also would like to point out that the incentives for each  
individual voter are strong. If you voted A=99, B=98 changing your  
vote to A=99, B=0 makes your vote 99 times stronger (assuming that A  
and B are the main candidates). We can expect that voters will be  
given advice to move to strategic voting. Parties that do that  
effectively will have better success than those that are not as  
efficient.

> (b) is entirely their own fault and hence is self-correcting over  
> time and not a
> valid attack on the voting system.
>
Do you mean that RV "self-corrects" itself to Approval. In that case  
the criticism of Range style voting is no more valid (except that  
maybe the trap of voting Range style could be removed by changing the  
system also formally to Approval). The vulnerability of "Range style"  
RV votes is still there.

> To see what I mean by (b) consider a Range Voting election.  Nixon  
> loses.
> The pro-Nixon voters complain:  "we foolishly did not indicate a  
> high preference
> for Nixon over Kennedy. But Kennedy Voters said they had high  
> preference the other way.
> So Nixon lost."   The response to this complaint:
> "It is your own fault idiots.  This is not the fault of the voting  
> system."
> Any court would throw this "complaint" out, and argue that Kennedy  
> SHOULD have won.
> It is rather like a bank complaining it was "robbed" after throwing  
> handfuls of
> dollars into the streets and then those dollars were unexpectedly  
> not returned
> by the pedestrians.
>
> In contrast, consider a Condorcet election.  Gore loses to Bush  
> thanks to a Nader spoiler
> effect.  The Nader voters complain "the voting system penalized us  
> for honestly ordering
> Nader top, Gore second. If we had had range voting we could have  
> expressed our
> honest ordering, without being penalized."
> That in contrast, seems genuinely the fault of the voting system  
> and not of the voters.
>
Should I read this so that RV may make a fair pick between Kennedy  
and Nixon if all voters vote in Approval style, and that Condorcet  
can also pick in addition to that also a compromise candidate  
(Nader). You didn't clearly mention what went (technically) wrong  
from the Nader voters' point of view. Maybe an example with  
percentages and voter preferences would help. My belief is that  
strategic voting is not very easy in large scale public Condorcet  
elections (although Condorcet methods can in some situations be (at  
least in theory, maybe in practice too) vulnerable to strategic voting).

My main comment was anyway that I found the claims of THE NATION  
magazine of RV having potential to become a "a strategic mess" not  
very surprising (didn't read the magazine though). Discussing also  
Condorcet vulnerabilities and comparing the problems and benefits of  
RV and Condorcet is also ok but that may be a long story.

Juho Laatu


> Warren D ?Smith
> http://rangevoting.org
> ----
> election-methods mailing list - see http://electorama.com/em for  
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