# [EM] Using weights to compensate multiple votes (It's mostly about PR)

Philippe Errembault phil.errembault at skynet.be
Wed Aug 25 03:25:03 PDT 2004

```I think there something I didn't realise before writing this...
I'm not in the frame of electing one! person and the point
is that it changes everything... Maybe I shouldn't have made
the analogy with approval system. PR systems are soooo
different from election for one person which are usualy
discussed here, that, maybe this group should be splitted
in two. the goals are absolutely not the same, nor the
consequences in the way of voting...

In fact, I'm trying to find a solution for a problem we have
in belgium with a proportionnal representation system...
In our country we vote for a specific party, and for a few
year we can now vote for multiple candidates from the same
party. This has consequences since it appears that people
voting for multiple candidates have more power than others,
but as another consequences, they may eventually also raises
the power of the party chosen order.

That's why I wondered how we could normalise the amount
of information contained in each vote.

because when voting for one person the problem I'm trying
to solve does not exist. But it exists with with PR, and you
are right with the fact that to try to solve it, we will have to
make a compromise with FBC. Now, with my system of
the computation of standard deviation, the less your favorite
candidate has votes, the less he will impact the major candidate.
even more : voting for all candidates BUT one of the majors,
could even strengthen your vote, because you would then
deviation would begin to lower.

Some people among us think that we just should divide the votes
by the number of candidates you favored (if you vote for N
candidates, each one will receive 1/N vote) but I think this is not
fair, since if you vote for each candidates but one in the list, your
vote will not express more than if you vote only for one candidate.
In fact you will favor the party order. By the way, this solution would
even be worse for the FBC.

Now a friend of mine observed that with my standart deviation system,
you can have a division by zero, if you voted for no candidates or for all
candidates. those two cases should be removed because they do not
favor any candidate. they should only be counted as votes for the list.

Philippe Errembault

the BELGIAN ELECTION SYSTEM :
In belgium, ballot papers contains lists from parties and for each
of them there is one chechbox called "la case de tête" (*) and
one checkboxes for each candidate.
(*) I don't know how to translate this... this is the checkbox, for
the whole list in the preference order favored by the party.
Someone helps ?

Voters can vote by choosing one party, then, they may vote for
the whole list (by checking the "case de tête") and/or they may
vote for any combination of  candidate of this party.

THEN, (I spare you the calculations) we compute how many seats
each party (p) will have (let's call it Np), and only then, we chose
who will be elected from each party, and that's the interresting point.

First of all, at the time our parliament decided to allow multiple votes,
they also decided to halve the effect of the "case the tête" you will
understand later why.

What happens, is that we give the votes from the halved "case de tête"
to the candidates from the top of the list, we see how many votes the
first one needs to be elected, and we give him what he needs, then for
the followers, until the pool is empty. Then we sort the candidates
according to the amount of votes they have.

Now the point is that with the possibility to vote for multiple candidates,
this will increase the number of candidates that will be helped by the "case
de tête" since, on the average, they will need less votes from the pool.
this is why they halved the effect of the "case de tête", but this seems not
to be sufficient, since for now, we have lists for which the "case de tête"
helped more candidates than the number that were effectively be elected
for this party (which means that all candidates were chosen in the party
favored order and none in the voters prefered order).

Another point is that voters from a specfic community can agree on voting
for all candidates from this community, on one specific party. (this is what we
often traditionnaly call a "stem blok" - from dutch). Doing that when the
people not members from this community can't make the same kind of
arrangement,  will drastically improve the chances for those candidates,
in fact, more than the real number of members of this community,

----- Original Message -----
From: "Warren Schudy" <wschudy at WPI.EDU>
To: "Philippe Errembault" <phil.errembault at skynet.be>
Cc: "election methods electorama" <election-methods-electorama.com at electorama.com>
Sent: Wednesday, August 25, 2004 2:44 AM
Subject: Re: [EM] Using weights to compensate multiple votes (Any feedback ? please !??)

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   |
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