Here is what I've just written for the new section titled "Multiple
rounds of voting":
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In highly competitive elections, multiple rounds of voting are needed to
eliminate the weakest candidates so that attention can be focused on
electing one of the most popular candidates. Our supported election
methods work as described for two rounds of voting if the first round of
voting elects a single winner from each political party, and the second
round chooses from among those winners.
However, different counting methods are needed if the same voters vote
in both rounds. There are election methods that handle such cases, and
they use the better ballots we support. However, we have not yet
analyzed this category of counting methods sufficiently to express
support for any specific methods.
We do strongly agree that single-mark ballots must not be used in any
round of voting. More specifically, just as the candidate with the most
first-choice votes is not necessarily the most popular, and the
candidate with the fewest first-choice votes is not necessarily the
least popular, the candidate with the second-most first-choice votes is
not necessarily second-most popular, and the candidate with the
second-fewest votes is not necessarily the second-least popular.
Also we agree that "open primary" elections are not fair. In this
approach, the candidates who are identified as "most popular",
regardless of political-party affiliation, progress to the next round.
This approach fails to consider that the majority of voters who support
the most-popular candidate are likely to be the same majority of voters
who support the second-most popular candidate -- unless the counting
method specifically compensates for this redundant influence. The
remaining voters, who may almost be a majority, can end up with only
getting to choose between the two candidates who are preferred by the
majority. Expressed another way, the words "most popular" are ambiguous
in the context of choosing which candidates deserve to progress to
another round of voting.
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I'm sure I'm missing some important additional considerations, but they
aren't coming to me at the moment, so I'll tap into your brains to help
refine this section.
Of course we aren't offering a fair way to handle French presidential
(?) first-round elections (in terms of which two candidates should move
on to the final runoff election), but we have nothing specific we would
agree on, right?
Richard Fobes
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