[EM] How to vote in Approval
Dave Ketchum
davek at clarityconnect.com
Tue Mar 26 20:25:09 PST 2002
On Tue, 26 Mar 2002 07:47:12 +0000 MIKE OSSIPOFF wrote:
> Demorep wrote:
>
> Mr. Ketchum wrote in part-
>
> Trying to be simple can be deceptive. Approval is easy to count,
> and sounds easy to vote until you have a ballot in your hands with a list
> of 4 lemons and need to decide how many of them you want to call
"approved".
> ---
> D- Approve NONE so that NONE get elected.
They are all lemons, to disapprove of, but there is more rot in some so I
want to help make sure those lose.
Also, there are various meanings of "NONE". "NOTA", which is used some
places, can be either:
An actual vote for NOTA as better than any of the live candidates.
An embarrassment to the politicians while leaving the election to
the other voters.
>
> I reply:
>
> Yes, don't vote for lemons. If some lemons are sourer than others,
> they're still all sour. A lesser-evil is still an evil.
As I said above, it can matter. Try actually destroying the country vs
getting a god start on that but leaving office with the country still in
recoverable status.
>
> I claim that, in our public political elections, there are always
> unacceptable but winnable candidates, and under those conditions,
> one's best Approval strategy is to vote for all of the acceptable
> candidates, and not for any of the unacceptable candidates.
>
> Under those conditions in a Plurality election, vote for whichever
> acceptable candidate is most likely to be able to be helped by you
> to prevent an unacceptable candidate from winning.
>
> Note how much simpler it is in Approval.
>
> What if all the candidates are unacceptable? Don't vote for any
> of them. The pitifully minimal gain from voting for the less
> disgusting one(s) isn't worth it. Don't validate that "choice" by
> voting among those candidates.
>
> If there are no absolutely unacceptable candidates, then strategy
> isn't so simple. But, if we have some sort of winnability information,
> as we do in our political elections, then if you'd vote for a lesser-
> evil in Plurality, vote for him in Approval too, but also vote for
> everyone whom you like better, including your favorite.
>
> Of course if there are unacceptable candidates, but they aren't
> winnable, then the above paragraph applies there too.
>
> What follows is for elections where there are no winnable unacceptable
> candidates:
>
> If there's no winnability information, that's called a 0-info
> election, and your best Approval strategy in public elections is
> to vote for all the candidates whose merit for you is above the
> mean.
>
> By the way, mathematical strategy has been discussed for when
> there's winnability information ("probability-info"):
>
> Preliminary definitions:
>
> Ui is the utility (worth) to you of candidate i.
>
> Pij is the probability that, if there's a tie for 1st place, it
> will be between i & j.
>
> The strategic value of candidate i is:
>
> The sum, over all j (j not equal to i) of Pij(Ui-Uj)
With my voter hat on I am unable to calculate the inputs to those formulas.
>
> In Approval, vote for all the candidates whose strategic value is
> greater than zero. In Plurality, vote for the candidate with highest
> strategic value.
>
> Someone pointed out that it's a fair approximation, when one doesn't
> have more accurate information, to say that Pij is proportional to
> the square root of the product of i's probability of winning and
> j's probability of winning. As an approximation one could say that
> the probability that i will be in a tie for 1st place if there is
> one is proportional to the square root of i's probability of winning.
> For Pij, multiply those tie-probabilities of i & j.
>
> The purpose of that is that it might be easier to estimate the
> candidates' probabilities of winning than it is to estimate the
> probability that i & j will be in a tie for 1st place if there is one.
>
> Derivation of that approximate way of estimating can be found
> at http://www.barnsdle.demon.co.uk/vote/sing at the Approval strategy
> page. In fact the other Approval strategy statements that I've made
> here are justified at that website. It needs to be updated. For instance,
> I sometimes used "frontrunner probability" interchangeably with
> "tie probability", and I haven't corrected that error at that website
> yet.
>
Summary:
I can understand the concept of holding Bush and Gore up to the
light and picking one as better/worse than the other - which is all I need
for ranked voting (unless it is a system that invites strategy).
Trying to decide whether I approve of them enough to list them for
Approval, especially with other candidates involved, is too much of a strain.
--
davek at clarityconnect.com http://www.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.
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