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Incomplete Election?


David A Foulkes

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Understood that in an election, barring any bylaw or rule otherwise, the election is incomplete unless one candidate receives a majority vote. On page 426, at line 27, RONR details the need for repeated revoting as needed when no majority vote is received. Lines 32-33 say "The same is true where two candidates tie for a majority vote for an office."

I'm unclear how this could happen, and would like to know under what circumstances it could.

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Understood that in an election, barring any bylaw or rule otherwise, the election is incomplete unless one candidate receives a majority vote. On page 426, at line 27, RONR details the need for repeated revoting as needed when no majority vote is received. Lines 32-33 say "The same is true where two candidates tie for a majority vote for an office."

I'm unclear how this could happen, and would like to know under what circumstances it could.

If several seats on a board or similar body are open, members can cast as many votes as there are seats open, so it is possible for two (or more) candidates to receive the same numbers of votes, and for each of them to garner a majority vote.

For example:

Three seats open, 100 legal voters casting, in total, 300 votes (i.e., no abstentions)

Candidate A: 60

Candidate B: 60

Candidate C: 60

Candidate D: 60

Candidate E: 30

Candidate F: 30

Candidates A, B, C and D have each received enough votes to garner a majority vote, but they are all tied. Since candidates E and F did not receive a majority vote, none of the six candidates have won a seat in this round.

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If several seats on a board or similar body are open, members can cast as many votes as there are seats open, so it is possible for two (or more) candidates to receive the same numbers of votes, and for each of them to garner a majority vote.

For example:

Three seats open, 100 legal voters casting, in total, 300 votes (i.e., no abstentions)

Candidate A: 60

Candidate B: 60

Candidate C: 60

Candidate D: 60

Candidate E: 30

Candidate F: 30

Candidates A, B, C and D have each received enough votes to garner a majority vote, but they are all tied. Since candidates E and F did not receive a majority vote, none of the six candidates have won a seat in this round.

I see. My cited sentence actually only applies to procedure #1, as noted on page 425 then. Frankly, I wasn't keeping that version in mind. Thank you.

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Okay, just a little problem I'm trying to work through. 100 voters, three offices open. I believe (though this is perhaps where I am going wrong) that no one can vote for the same person on the same ballot. That is, you can vote for any three of the candidates, one entry for each. But you can't vote for A, A and B. So, some simple math for example:

60 members vote for A, B, and C. That leaves 40 voters to cast votes for D, E and F. Therefore, D cannot get 60 votes also.

I've tried a few different permutations and can't make it work. Even if you bring it down to 51 voters for A, B, C (thereby getting a majority threshold), that leaves 49 voters left for D, E and F. And I can's seem to make it come out a four-way tie.

Thoughts?

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Okay, just a little problem I'm trying to work through. 100 voters, three offices open. I believe (though this is perhaps where I am going wrong) that no one can vote for the same person on the same ballot. That is, you can vote for any three of the candidates, one entry for each. But you can't vote for A, A and B. So, some simple math for example:

60 members vote for A, B, and C. That leaves 40 voters to cast votes for D, E and F. Therefore, D cannot get 60 votes also.

I've tried a few different permutations and can't make it work. Even if you bring it down to 51 voters for A, B, C (thereby getting a majority threshold), that leaves 49 voters left for D, E and F. And I can's seem to make it come out a four-way tie.

Thoughts?

Each member casts three votes for different candidates. So, there are 300 hundred possible votes to be cast.

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Each member casts three votes for different candidates. So, there are 300 hundred possible votes to be cast.

Voters 1-15: A, B, C

Voters 16-30: A, C, D

Voters 31-45: A, D, E

Voters 46-50: A, E, F

Voters 51-55: A, D, F

Voters 56-60: A, B, F

Voters 61-75: B, C, F

Voters 76-90: B, C, D

Voters 91-100: B, D, E

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Very neat!

I agree. Thank you to Mr. Elsman for the concrete illustration.

I remember working through a similar situation in response to a post a few months ago, and eventually, by trial and error, finding a combination of votes which added up properly. I strongly suspect there's a mathematical proof that all possible distributions of vote counts are indeed possible, so long as you don't disobey the basic limiting conditions (in this instance: no more than 300 votes total; no more than 100 votes for any one candidate). I don't know how to approach the proof though, or what branch of mathematics this falls into.

edit:

"all possible distributions of vote counts are indeed possible"

That sure sounds dumb, on re-reading, like demonstrating that '0=0'

-- hopefully clearer to say:

"all imaginable distributions of vote counts are indeed possible"

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I agree. Thank you to Mr. Elsman for the concrete illustration.

I remember working through a similar situation in response to a post a few months ago, and eventually, by trial and error, finding a combination of votes which added up properly. I strongly suspect there's a mathematical proof that all possible distributions of vote counts are indeed possible, so long as you don't disobey the basic limiting conditions (in this instance: no more than 300 votes total; no more than 100 votes for any one candidate). I don't know how to approach the proof though, or what branch of mathematics this falls into.

It was demonstrated in "Multiple Candidate Election Surprises," Parliamentary Journal, April 2010.

It demonstrated that, in a ballot vote where multiple candidates run for multiple seats:

1. A candidate could get a majority, and not be elected.

2. A candidate could be unopposed (only enough people running to fill the available seats), no write-in candidate, and still not get elected.

Edit: No illegal votes or illegal voters either.

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