[EM] The general form of Quick Runoff

[C.Benham]

Juho wrote (23 May 2010):

<snip>

>/ 1. Rank the candidates. Truncation is allowed. Equal ranking is not
/>/ planned for (but we could come up with something).
/>/ 2. Label the candidates A, B, C, ... Z in descending order of first
/>/ preference count.
/>/ 3. Let the current leader be A.
/>/ 4. While the current leader has a majority pairwise loss to the very
/>/ next candidate, set the current leader to the latter candidate. (In
/>/ other words step 4 must be repeated until there is no loss or no other
/>/ candidates.)
/>/ 5. Elect the current leader.

/

>How about this example and LNH.
>
>6: A>C
>5: B>A
>2: C>B
>2: C
>
>Candidate names indicate the order in first preferences. B beats A. C  
>beats B. C wins.
>
>6: A>C
>5: B>A
>2: C>B
>2: C>A
>
>Two "C" voters have changed their vote to "C>A". B does not beat A. A  
>wins. The "C" voters were harmed when they included their later  
>preferences.
>
>Juho
>
>  
>

Juho,

The key word you missed in the definition is "majority". In both your 
elections there are 15 ballots, so a
"majority pairwise loss" requires a winning score of at least 8.

In both cases the FPP winner A wins, in the first because B's pairwise score against
A is 7, a pairwise win but not a "majority" pairwise win (and so of course not a 
"majority pairwise loss" for A).


Chris Benham


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