# Proportional Representation via Approval Voting (fwd)

DEMOREP1 at aol.com DEMOREP1 at aol.com
Thu Jan 18 21:27:02 PST 2001

```Mr. Layton wrote in part --

I made up a fairly random (ordinal ranking) voting pattern with 8

candidates.  I assure you, it was the first (and so far only) example I

tried, so it isn't contrived in order to prove a point.  The eight

candidates are ranked by an electorate of 100 voters in the following way;

30 A>B>C>D>E>F>G>H

10 B>F>G>D>A>H>C>E

5  C>H>D>F>G>A>B>E

5  D>B>A>H>C>E>G>F

15 E>D>A>F>H>B>G>C

10 F>E>B>G>A>D>C>H

5  G>A>E>B>H>C>D>F

20 H>G>F>E>D>C>B>A

There are to be three winners.
----
D- Again - The math for single winner elections also applies to multi-winner
elections.

A YES/NO vote on each choice will show if any of the choices gets a Droop
Quota of YES votes -- more likely obviously with party groups.

Condorcet (head to head) math also applies to p.r. elections.

For all combinations--
N test winners versus test loser (all others deemed losers)

If a choice wins in ALL of his/her combinations when he/she is a test winner,
then he/she is a p.r. Condorcet winner.   Any choice getting a Droop Quota of
first choice votes is obviously a p.r. CW.

Testing A,E,H versus F

A 30 + D 5 + G 5 = 40
E 15
H 20 + C 5 = 25
----
F 10  + B 10 = 20

All combinations would need to be done (requiring computerized votes for
large elections).  Even the above 8 choice example is a major chore if done
manually.

Real elections would have party groups.  N1 A>B>C, N2 B>A>C, N3 A>C>B, etc.
There could and should be a party vote.

A tiebreaker-  sum the place votes (1st, 2nd, etc.) to get the earliest Droop
quotas.

In case of ties, the earlier votes would count.

Votes for the losers would go to the earliest winner on the ballots.

Each winner would have a voting power equal to the votes he/she finally

Even the smallest legislative body should have perhaps at least 5 members (to
lessen the chances of having 1 choice getting a majority of the votes).

Such a tiebreaker would have an element of plurality-- however for
legislative body elections the problems with plurality are quite a bit reduced
(since major factions will be electing one or more of their choices).

```