Talk:IRV Prime: Difference between revisions

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The problem is, such a profile P may make it impossible for c to become the Condorcet winner; looking at all the profiles P where a wins (we must increment by 2 otherwise we continue to have a tie):

(updating to use N to hopefully become clearer --[[User:Marcosb|Marcosb]] ([[User talk:Marcosb|talk]]) 21:52, 4 August 2021 (UTC))

P1:

{{ballots|

abc: 5

abc: 3N + 2

acb: 2

acb: 2N

bca: 3

bca: 3N

bac: 2

bac: 2N

cab: 3

cab: 3N

cba: 2}}

cba: 2N}}

P2:

{{ballots|

abc: 3

abc: 3N

acb: 4

acb: 2N + 2

bca: 3

bca: 3N

bac: 2

bac: 2N

cab: 3

cab: 3N

cba: 2}}

cba: 2N}}

P3:

{{ballots|

abc: 4

abc: 3N + 1

acb: 3

acb: 2N + 1

bca: 3

bca: 3N

bac: 2

bac: 2N

cab: 3

cab: 3N

cba: 2}}

cba: 2N}}

It becomes clear that in Profile P results in some unavoidable truths:

* If we add only a single abc or acb vote, a loses to or ties with c (a=7N + 1, c = 8N); so we must add 2

It becomes clear that in Profile P where a tie is broken & a wins, a wins because they are the Condorcet winner, so it cannot be true that c is the Condorcet winner.

* For N=1, a is the Condorcet winner (& the premise "c is the Condorcet winner" does not hold); for any N>1, a loses to c (& thus the premise "a wins in P" does not hold)

* If we add 2N instead of 2 (to meet the premise "a wins for all N"), then a becomes the Condorcet winner for all N

--[[User:Marcosb|Marcosb]] ([[User talk:Marcosb|talk]]) 17:20, 4 August 2021 (UTC)