[EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Abd ul-Rahman Lomax]

At 01:23 PM 6/17/2013, Jameson Quinn wrote:

>2013/6/17 Benjamin Grant <<mailto:benn at 4efix.com>benn at 4efix.com>
>
>Is *this* an example of Bucklin failing Participation?
>
>5: A>B>C
>
>4: B>C>A
>
>A wins
>
>Right
>
>But add these in:
>
>2: C>A>B
>
>  B wins.
>
>
>Yes, with your "tiebreaker".

This is not participation failure. Adding ballots ranking C highest 
did not cause C to lose.

By the way, an oddity about this example. Bucklin is ranked approval. 
Did all the voters approve all candidates?

Round 1. Majority is 5

A wins in round 1.

Adding the2 voters, majority is now 6.

First round:
A: 5
B: 4
C: 2

no majority, go to next round.

Second round:
A: 7
B: 4
C: 6

A still wins. B does *not* win. Bucklin terminates when a majority is found.

Participation criterion from previous post: "Adding one or more 
ballots that vote X over Y should never change the winner from X to Y"

Showing the third preferences is confusing and irrelevant. I do not 
know why Jameson approved "B wins." But even if B had won, it would 
not have shown participation failure. The vote must change the result 
away from C to another winner.

One fact that should be understood about Bucklin: first of all, 
Bucklin votes are *approvals*. Every explicit Bucklin vote is voting 
*for* the candidate under the condition that the rank has been 
reached in the amalgamation process.

Secondly, a Bucklin ballot is a *Range* ballot, covering the approved 
range only. So ranks may be left empty. Bucklin is *not* a pure 
ranked system. So if a voter has A>B>C, the voter will *not* vote for 
all three, unless there is some other worse candidates, or the voter 
really does want to completely stand aside from the election. And 
that doesn't work with respect to write-in candidates....

So if the voter has preferences A>B>C, the voter may vote, in the 
form of Bucklin we generally are working with, called Bucklin-ER 
(equal ranking), these votes, and all could be sincere:

A
A>B
A>.>B (blank second rank)
A=B

This *assumes* that there is a third candidate, C, that is least 
preferred. If there are four candidates (or more), the voter can have 
*many more sincere voting patterns*.

Each pattern has implications about *preference strength*. That is 
part of why I say that Bucklin uses a Range ballot.

Suppose that the voter *really prefers* a candidate not on the 
ballot, and wants to vote for that candidate, we'll call W.

W
W>A
W>A>B
W>A=B
W>.>A
W>.>A=B
W=A>B
W=A>.>B
W=A=B

Just to make this clear.