[EM] Proportional Representation via Approval Voting

[Forest Simmons]

Hi, thanks for your response.

On Mon, 15 Jan 2001, LAYTON Craig wrote:

> Hi Forest;
> 
> I'll need to think more about this.  Do you know what advantages this system
> has over STV or standard list pr (like d'Hondt)?
> 

The advantages are largely unexplored. But there are some obvious ones,
for example, existing voting machines for traditional plurality
multiwinner elections could be used without modification to collect the
approval ballots.  Also, like STV, the candidates could all run without
declaring any affiliation with any party.  In other words, the votes of
like minded people automatically define the (possibly overlapping)
affinity constituencies in many more ways than could ever be sorted out by
organizing special parties for the various flavors of voters. 

Since this method is a fairly direct and simple generalization of standard
approval voting (in which all of the layers receive the same weight) I
would imagine that some of its favorable characteristics would be
inherited.. My feeling is that PR through approval is more apt to take
advantage of overlapping constituencies; the central, moderate candidates
are not as likely to be eliminated.  But I could be wrong.  Even if I am
wrong, the multiple application of the method in stages to get a core
group of moderates is more seamless and less ad hoc than similar remedies
for the STV.

Actually, I'm proposing a whole class of multiwinner voting methods. Every
sequence of decreasing positive weights for redundant "layers" defines a
member of this class.  For example, if the sequence is the square of the
harmonic sequence 1, 1/4, 1/9, ... 1/k^2 ... then like minded segments of
the electorate would be represented in proportion to the square root of
their size.  This would be appropriate in a system where it is desirable
for various constituencies to have power (defined as the probability that
their representatives' votes will make a difference on a typical motion)
in rough proportion to their size (according to the square root rule of
block voting power).


> The fact that
> this is highly unlikely if voters use strategy and available polling
> information isn't good enough in my opinion.

In this regard I would like to point out that the corporate media treats
the presidential race like a horse race.  The issues are avoided.  All of
the information is about who is ahead.  In the balance between information
needed for Cardinal or Ordinal Rankings and the information for
strategizing, the scales are tilted towards the latter (to the degree that
these kinds of information can be separated.)

Thanks for your interest and valuable questions; whoever leads me to the
Achilles heel of an idea is as good a friend as one who encourages me to
keep trying.

Forest




> 
> -----Original Message-----
> From: Forest Simmons [mailto:fsimmons at pcc.edu]
> Sent: Saturday, 13 January 2001 9:05
> To: election-methods-list at eskimo.com
> Cc: Francis Edward Su; Steven J. Brams
> Subject: [EM] Proportional Representation via Approval Voting
> 
> 
> Just as the STV system of proportional representation uses the front end
> of the Borda Count (ballots with the candidates ranked), so can the front
> end of Approval Voting (ballots marked with approved candidates) be used
> to achieve another system of proportional representation. 
> 
> Think in terms of layers.  If you are bundling up for extreme cold, the
> more layers the better, but the first one or two layers count the most; it
> doesn't do much good to add a third layer of sweaters for the torso if the
> legs are still uncovered. An extra pair of mittens is good, but that first
> pair of ear muffs is more urgently needed.
> 
> The layers of protection for various body parts are analogous to layers of
> representation for the various parts of the body politic. (And just as
> long johns cover arms, legs, and torso, so some candidates may represent
> more than one segment of the electorate.)
> 
> Various multiwinner systems of voting can be specified by assigning
> various weights to the various layers.
> 
> It turns out that for proportional representation, the nth layer must
> receive 100/n percent of the weight of the first layer.
> 
> For example, in any multiwinner election having six or more positions to
> be filled, the sixth layer should count only one sixth as much as the
> first layer.
> 
> In general we have n positions to be filled from among N candidates. Let C
> be one of the N!/n!/(N-n)! possible combinations (coalitions) of n
> candidates, and let B be one of the approval ballots cast in the election.
> Suppose that ballot B approves exactly k of the members of the coalition
> C.  Then this ballot contributes support for this coalition in the amount
> 1 + 1/2 +...+ 1/k .
> 
> The coalition with the highest total wins the election (unless side
> conditions are not met).
> 
> A side condition might be, for example, that no one approved by fewer than
> 1/(n+1) of the voters could be elected. This reduces to requiring majority
> approval in a single winner race. This condition is easily incorporated by
> eliminating such candidates before examining the various possible
> coalitions. 
> 
> Another side condition might be that the candidate with the greatest
> over-all approval should be in the winning coalition. (This is not
> automatic.) This side condition would be appropriate if the winning
> coalition is to be the entire government, and one member of the coalition
> is to be the moderator or president. 
> 
> This condition can be incorporated by automatically including him in all
> of the coalitions to be evaluated. In other words, every admissible
> coalition is made up of the most popular candidate and n-1 other
> candidates.
> 
> If there are three positions of preeminence, say a triumvirate, the method
> can be used to choose the coalition of three first, and then another
> application of the method in which every admissible coalition contains the
> winning three and n-3 other candidates.
> 
> If the triumvirate is to have a distinguished member, three successive
> applications of the method to the voted ballots would do the trick; the
> first round picks the prez by restricting all coalitions to one member.
> The second round restricts coalitions to three members, one of which is
> the prez.  The third round considers only coalitions containing the
> triumvirate.
> 
> Note that the same ballots (without alteration) are used in all three
> rounds.
> 
> Well, that pretty well describes the voting procedure.
> 
> If you want the gory details of some examples and a proof of the
> proportionality property, I'll post another message next time. 
> 
> I hope you like it.
> 
> Forest
> 
>