[EM] Sunday reply to Bill Lewis Clark

Bill Lewis Clark wclark at xoom.org
Mon Jan 19 13:34:26 PST 2004


> Does your Approval strategy involve rounding off?

Approval can be thought of as a rounding up or down of Cardinal Ratings /
Range Voting to the maximum or minimum values of the range.  My example of
the rainfall measurements was meant to draw attention to the ways in which
rounding off values can cause you to lose important information.

However, as Bart Ingles pointed out in an earlier reply to my original
post, the proper way to convert between sincere Approval preferences and
sincere CR/RV preferences is to use a probabilistic model, not a simple
roundoff mechanism like I'd been assuming.

Voters who sincerely prefer A:10, B:9, C:0 should be broken down into 90%
sincere AB approvers and 10% sincere A approvers -- NOT into 100% sincere
AB approvers (which is what I've been assuming until now.)  Bart actually
made this point in relation to an example where a particular candidate had
sincere support that was 50% of the maximum (and should thus be sincerely
approved and sincerely disapproved by equal numbers of voters.)  However,
the point holds even in the more extreme cases.

Given that the probabilistic assumption holds in even the extreme cases,
I'm almost positive my entire argument completely falls apart.  Here is a
more detailed breakdown:

Voters using an optimal strategy will always vote at the maximum or
minimum of the allowed range, for each candidate (NOTE: this does not in
itself imply that Approval and CR/RV are strategically equivalent, because
there's no guarantee that CR/RV voters will give maximum and minimum
ratings to the same candidates they would approve or disapprove,
respectively.)  Sincere voters might use intermediate values.  *IF* those
sincere votes suffered from a sort of "roundoff error" during conversion
from CR/RV to Approval, this might distort the overall distribution of
voter preferences such that Approval and CR/RV would require different
optimal strategies.  (The example I provided in my post earlier today
demonstrates a situation in which the overall distribution of voter
preferences undergoes significant change depending upon what percentage of
voters are sincere, resulting in changes in the optimal strategies for the
remaining strategic voters -- I thought something similar might happen
because of this "roundoff error.")

It's that assumption of "roundoff error" that is flawed.  So long as there
are enough voters so that a smooth probability distribution can be
assumed, Approval and CR/RV should provide equivalent situations for
strategic voters.  (NOTE: although Approval can still be thought of as
rounding off CR/RV ratings to the minimum or maximum values, no "error"
occurs because of the way in which these min/max values get averaged
together via the probable distribution of voters.)

My original claim is quite possibly true in extremely limited cases -- for
example, if there is only one voter with a sincere preference of A:10,
B:9, C:0 then when the conversion to Approval takes place, we'll have
either 100% sincere AB approval or 0%, and that *could* result in
differing optimal strategies for Approval and CR/RV in those circumstances
(if that single voter is decisive.)  However... that's such a ridiculously
unlikely scenario that I'm not going to claim it as any sort of support
for my argument (I'm just pointing it out as a curiosity more than
anything else.)

> If you believe that someone's optimal strategy in a CR election is
> different from what it would be in the series of identical Approval
> elections, then is there some reason why you don't want to tell us
> exactly why you believe that?

I thought that's what I was doing, but apparently I wasn't being as clear
as I thought.  Hopefully the above explanation lets you see how my
reasoning went (and where it went wrong.)

> I take it that you're assuming that what Democrats will do in office
> is the same as what they advocated in their election campaigns :-)

Not at all; that's why I'm supporting Kucinich instead of Dean.  I don't
particularly trust either of them -- but Kucinich seems to have a better
track record of following through with unpopular stances.  Not that
election reform is particularly unpopular... but I'm not taking any
unnecessary chances. :)

> You argued that IRV will work well because 3rd parties are small.
> So you agree that the sure-loser status of parties other than the
> Democrats & Republicans is necessary to defend IRV.

Well, I'm not so sure the Democrats and Republicans will always be the two
major parties, but I do agree with the point that IRV suffers from a type
of spoiler effect.

I still feel that IRV better than Plurality, given the existing political
climate.  Right now, voting for a third-party candidate is somewhat likely
to result in your least-favorite major party candidate winning the
election.  That wouldn't happen under IRV -- given that we currently have
no "big" third-parties.

I'll grant you that IRV would present some nasty problems down the road --
some of them arguably more troublesome than those Plurality causes -- but
there's no reason IRV couldn't be used as a stepping stone to later
changes to an even better system.

Why not simply support that better system *now*, and forget about IRV
altogether?  Because IRV has more popular support.  We still have a
Plurality system, and I'm simply exercising my optimal strategy by
supporting the front-runner I dislike least.

> Thanks, but no thanks. Just what we need: Having bunglers pave the way
> for us.

Mike, what's your beef with IRV?  I mean, your hostility seems to go well
beyond a technical dislike -- it seems personal.  Did some misguided IRV
supporter in your past shoot your dog, or something?  Just wondering.

-Bill Clark

Dennis Kucinich for President in 2004

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