DEMOREP1 at aol.com DEMOREP1 at aol.com
Sun Apr 9 15:38:48 PDT 2000

```The use of a YES votes tiebreaker versus a head to head tiebreaker also comes
up in the context of a proportional representation (p.r.) election having
subgroup circular ties.

A small party may barely get a Droop quota of the votes. Three or more of
such small party's p.r. candidates may be in circular tie for 1 or more seats.

Assume that if YES votes are used, then only the real supporters of such
party have voted YES for 1 or more of such 3 or more candidates.

However, if head to head is used as a tiebreaker (worst defeat loses), then
the supporters of the other parties (the majority) may determine which
candidate from such small party (a minority) is chosen.

Backing up to the single winner case (which is the limiting case of the
general N winners case)----

N1 ABC
N2 ACB

N3 BAC
N4 BCA

N5 CAB
N6 CBA

N1 + N2 = A1
N3 + N4 = B1
N5 + N6 = C1

A1 + N5  A
B1 + N6  B

B1 + N1  B
C1 + N2  C

C1 + N4  C
A1 + N3  A

YES votes (assuming first choice and second choice position votes are YES

A1 + N3 + N5    A
B1 + N1 + N6    B
C1 + N2 + N4    C

In real elections, of course, only some of the position votes may be YES

Compare the 2 groups of votes.

Thus, should (a) the NO majority voters determine who wins in a p.r. election
or (b) the NO minority voters determine who wins in a single winner election
???

The answer would seem to be No in both majority-minority directions.

Of course in both cases, if a voter is not sure what is going to happen
regarding which candidates can get a YES Droop Quota (which is a majority in
the single winner case), then such voter might vote YES on additional choices
based on the often mentioned-

desired > compromise > opposed

```