[EM] Median-based Proportional Representation

[Warren Smith]

[Minor bug in Jameson;s claims: I think he meant >=N not >N.]
[Major ambiguity in Jameson's post: when you say "given rating" did
you mean this rating
is allowed to depend upon the party, or must it be  party-independent?]

The RRV PR-theorem was if the voters all are "totally racist" that is vote
max-score for their color, and min-score for all others, then the
winners will have the same
color fraction as the voters (if enough candidates run from each
color, and up to
integer roundoff effects). Further if any particular party has
at least N droop-quotas worth of total-racist supporters, they'll win
at least N seats.

If RRV voters merely vote at least X times higher score for their
color than any other color,
that by itself will not assure PR.  For example if the red voters
voted 0.001 for each red and
0.000001 for each non-red, that'd have little effect on helping reds win seats.

The STV PR guarantee is pretty much the same as the RRV one, that is,
the "racist"
voters need to vote their color absolute top, all rival colors non-top.

Incidentally in RRV and STV, the "colors" do not need to have anything
to do with parties.
They can be an arbitrary coloring.

In AT-TV, suppose
30% of the voters vote Red=9, Blue=Green=0;
30% of the voters vote Blue=9, red=green=0;
40% of the voters vote Green=5, red=green=4.
Will it then elect 30% reds, 30% blues, and 40% greens?
And do you consider that the right thing to do?


On 7/9/11, Jameson Quinn <jameson.quinn at gmail.com> wrote:
> 2011/7/8 Warren Smith <warren.wds at gmail.com>
>
>> Sorry, as Jameson pointed out, he has invented a voting method he calls
>> AT-TV
>> which (he claims)
>>  1. obeys a proportional representation theorem
>
>
> Yes. It's instructive to see what PR criterion AT-TV satisfies, and what RRV
> satisfies.
>
> The standard Droop criterion, if I'm not mistaken, is: If a group of N droop
> quotas of voters votes a set of >N candidates above all other candidates,
> then at least N candidates from that set must win.
>
> The AT-TV version would be: If a group of N droop quotas of voters votes a
> set of >N candidates at or above a given rating, and all other candidates
> below that rating, then at least N candidates from that set will win.
>
> The RRV version... well, I'm not sure, but my guess is that it would be
> something like: If a group of N droop quotas of voters votes a set of >N
> candidates each with at least N times the rating of any candidate outside
> that set, then at least N candidates from that set must win.
>
> Note that these are successively weaker criteria on the systems; that is,
> the coordination of a given party must be successively stronger to ensure PR
> for that party. Purely on a subjective level, I think that AT-TV criterion
> is about right, and that the RRV one is too weak.
>
> JQ
>


-- 
Warren D. Smith
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