Talk:IRV Prime: Difference between revisions
Better premise with N
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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:
acb:
bca:
bac:
cab:
cba:
P2:
{{ballots|
abc:
acb:
bca:
bac:
cab:
cba:
P3:
{{ballots|
abc:
acb:
bca:
bac:
cab:
cba:
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
* 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)
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