Why Republicans should want range voting (Executive summary)
Republicans and the USA were hurt by Plurality voting
in 1912 when it caused Woodrow Wilson to be elected
instead of Theodore Roosevelt, then in 1920 when
the backlash from that error allowed/caused the election of Warren G. Harding,
widely regarded as the worst president in US history.
The Republicans may also have been victimized by Plurality in
1992 when Bill Clinton was elected instead of Robert Dole.
In general the better candidate usually loses in a 3-way race
because he splits the vote with a popular and similar third-party
(who is probably more similar to the better candidate, since
that was why he was popular).
Range voting fixes that pathology. The cost of
even a single one of these bad events hugely exceeds the
cost of switching to range voting.
Even without fixing the USA's system – just doing your own primary elections
via range voting (much easier task) – you will be able to get ahead and enjoy
huge long-term advantages over the Democrats, including significantly better chance of winning
the presidency. As a start we suggest trying this in Iowa 2008. You are going to need it.