# [EM] Strategies for RRV/RSV and BR for multi-member constituencies

Raph Frank raphfrk at gmail.com
Wed Jan 28 09:50:58 PST 2009

```http://www.rangevoting.org/RRV.html

I wonder what would be reasonable strategies for RRV.

Initially, I was thinking something like

"Set the approval threshold where you would set it in normal approval
but only include candidates from your favourite party of those that
have a reasonable chance of winning a seat"

This would mean that you would still approve candidates from a party
you like but who don't have a chance of winning a seat.

Assuming N=number of seats to be filled, another would be

"Of the the N+1 most likely candidates to be elected, approve N of
them and also approve all candidates you prefer to the 2nd least
likely of them to get elected"

In the N=1 case, this collapses to the standard

"Of the 2 most likely candidates to be elected, approve 1 of them and
also approve all candidates you prefer to the most likely of the 2 to
get elected"

I wonder if the interative effect of using that strategy, assuming
honest polling data, is to converge on one of the condorcet like PR
methods.

Anyway, testing strategies is hard for multi-winner elections as there
is no simple rule like BR.  Previously, there has been some
suggestions on how to handle PR-elections including virtual
parliaments and multi-dimensional issue spaces.

An easy option is to just average the utility of all the winners.
However, this doesn't take into account the benefit of diversity of
candidates elected, which is one of the big points of PR.

A method that elects candidates with utilities of

0,10,20,30,40,50

will count as the same as one that elects candidates with utilities of

30,30,30,30,30

However, the first is more likely to be a PR result.

One option would be to take the median candidate for each voter as his
utlity for that result.  This somewhat simulates the concept that a
legislature follows the median member.

OTOH, since the legislature is likely to be much larger than the
district in question, maybe each elected candidate can be considered
as independent.  If one member of your party gets elected from your
district, then that increase the probability of that party getting
into government by X%.  It is likely that if 2 members of the party
get elected, it will raise the probability by 2 times X% (plus a small
extra amount).  Thus, the utility of each member of the party getting
elected adds linearly.  Any non-linearility should be small especially
if the number of seats to be elected is kept low.

Thus, maybe just summing/averaging the utilities of all the winners is
the correct option (even though I don't really like it).

The only exception is if your party has no seats at all.  In that
case, the first member being elected would be worth alot.  However,
that just means that you would have high utility for that candidate
and anyway, your party would only be able to run 1 candidate in your
district, if it was small.

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