[EM] Straight Approval or PAV?

Gervase Lam gervase.lam at group.force9.co.uk
Sat Mar 18 09:47:58 PST 2006

As many some people may know, the World Cup will take place in Germany
during June/July this year.  Many of the top national soccer teams have
qualified for the World Cup, including Brazil, Italy and England.

Before the competition starts, the coaches of each of the national teams
must select a roster/squad of players to take to Germany.  Being on a
mailing list that involves one of the qualified teams, I have been
thinking of doing a poll to see what players people think should be in
the roster/squad.

My initial thought is to use an Approval method and not a ranking
method.  The reasons are as follows:

(1) The squad will contain about 20 players and I can't imagine how
anybody can give me an accurate ranking of about 10 let alone 20

(2) Just having the voters select players makes their life easier.  Then
they would not have to ask questions like "Should I rank this player
above this other player?" etc...

(3) Makes counting easier.  I don't want to write a computer program
just to count the ballots.  With Approval, I could probably just put the
ballots into a single file and then use something to sort the candidates
in alphabetical order.  From that, I could do a count.

(4) I think using ranking is probably taking this poll too seriously.

Considering that this poll will have multiple winners, my thoughts went
into thinking about Proportional Approval Voting (PAV).  Forest Simmons,
Joe Weinstein and others discussed this a while back.  However, Joe made
the following point that generally summarised the reasons for having
multi-winner methods:

> [EM] Discounted Redundant Layers 
> Joe Weinstein
> Tue, 16 Jan 2001 02:18:13 -0800

> it is a widespread myth that aggregate or 'social' utility (of a given
> panel or single candidate) should be taken as the sum of individual
> voter utilities (for that panel or candidate).  This myth would have
> us believe that - for a given single candidate or panel - if each
> grade does (or could) express the voter's utility (in some sense) then
> the sum total of the grades should express social utility.  Now, for
> many of us this myth is clearly erroneous, because we perceive social
> DISutility arising from unequal allocation of aggregate utility.  In
> brief, a situation in which everyone is equally satisfied seems, on
> balance, somewhat more satisfactory overall than a situation in which,
> though average satisfaction is a bit higher, a large fraction of the
> people are far less satisfied than average.

What Joe is saying is that for a multi-winner chamber, the aim is to
satisfy as many of the voters as possible.  However, in my case the aim
is to find the best players.  So, voter satisfaction is a lower
priority?  In other words, I should be aiming for high average utility
in the poll?  Any have any opinions about this?

Assuming that I use straight Approval, I would not be surprised if some
of the top candidates get 100% approval.  Really, the interesting part
is at the 20 player cut-off.  In other words, who would miss out from
being in the squad.

Also, the candidate 'spectrum' will be interesting.  In a chamber, you
want good left and right wing representation, for example.  Generally,
each voter will vote in a left OR right wing way.  Each voter doesn't
vote for a wide variety of left and right wing candidates.

However, for the poll, I expect each ballot to have a large variety of
players.  For example, on each ballot, there could be a player who is
good at jumping and heading the ball into the goal to score AND a player
who is good at dribbling the ball into goal.  This gives the squad a
good variety of goal scoring players.

There may be voters who don't vote for the good dribblers because this
is not the style of play the voter wants the team to have.  I don't
think this will occur often if it all.  But you never know...


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