# [EM] Using weights to compensate multiple votes (Any feedback ? please !??)

Warren Schudy wschudy at WPI.EDU
Tue Aug 24 17:44:43 PDT 2004

```As I understand it, your scheme, unlike regular approval, fails the
Favorite Betrayal Criterion (FBC). Suppose there is a close race between
two major candidates, call them Bush and Kerry. Suppose a voter has a
favorite that is neither Bush nor Kerry. In regular approval, a rational
voter will vote for their favorite and the better of the big two. In your
scheme, the rational voter will abandon his/her favorite, voting for just
the major candidate, since that reduces the information in the vote,
increasing its weight.

I also don't understand what problem you are trying to solve. Voting for
multiple candidates doesn't really give you more power in regular approval
voting - for any pairwise contest, you can only tip the balance by 1
vote either way, regardless of how you vote. Can you give an example of an
election where the wrong candidate was elected (in your view) because of
the extra power high-information ballots have?

BTW, I just noticed that (regular) approval is equivilant to Condorcet
methods with the stipulation that all voters must consider all candidates
to be in one of two equivilant sets (aka dichotomous). This is very
similar to a statement in the book "Approval Voting", by Braham or
something.

-wjs

On Wed, 25 Aug 2004, Philippe Errembault wrote:

> I'd like to get feedback on this topic, please...
> It's about normalising the enthropy (amount of information)
> contained in of an "approval like" vote.

>   ... But since english is not my mother tongue and since you write much
> ;-) and since there is only 24h in a day and since blah blah blah ;-)
> ...
>
>   I'd like to have your opinion about an idea concerning the impact of
> voting for multiple people :
>
>   In any approval-like system, where you can give your voice to more
> than one candidate, you have a problem since giving voices to multiple
> candidate raises the weight of vote. Especially if a group of voters
> give their voice to the same specific group of candidates, the will
> drasticly raise the chances of all their vote to match with other voters
> who didn't arrange with them.
>
>   So, why not evaluate the amount of information (let's call it [I])
> contained in a vote, and weight this vote by 1/[I] !?
>
>   first idea : let's give the value 1 to each approval to a candidate
> and 0 for others. the vote will then be a set of 1 and zero, for wich we
> can compute the average, variance and standart deviation. Let's use
> standard deviation for [I] and each vote by 1/[I].
>
>   this reduces impact of explicit arrangement, but not for implicit
> arrangements : let's call implicit arrangement, the fact that a well
> known has more chances than others to accumulate random votes, so people
> voting for them will have more chances to match other voters.
>

/-----------------------------------------\
| Warren Schudy                           |
| WPI Class of 2005                       |
| Physics and computer science major      |
| AIM: WJSchudy  email: wschudy at wpi.edu   |
| http://users.wpi.edu/~wschudy/          |
\-----------------------------------------/

```