[EM] YES versus Head to Head Tiebreakers

[DEMOREP1 at aol.com]

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

Head to head

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 
votes).

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 
votes.

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