By Warren D. Smith 2007
I believe IRV leads to 2-party domination(2PD) while delayed (second round) top2 runoff leads to more than 2 powerful parties. I'll discuss evidence.
Warning: This evidence is oversimplified because there are other factors involved which we have not discussed. For example, many countries have several voting systems and looking at the IRV and TTR seats only (which is what we do) is thus only part of the picture; some countries have ethnic or linguistic subgroups which cause multiparties or two parties naturally to exist. A less simplistic examination would try to disentangle these factors, if possible. However, let us just note that Fiji evolved 2PD under IRV despite several ethno-lingual groups and a quota system of seats for each, and Australia evolved 2PD under IRV despite also having PR seats (multiparty) in its upper houses. The USA, without these multiparty-genic factors, therefore would be even more expected to stay in 2PD status if it switches to IRV.
IRV is used in
Ireland (president)
Australia (House)
Malta (actually, uses STV in multimember districts and no longer uses IRV since no longer any
single-member districts)
Fiji (but there was a coup in 2006-2007 which ended democracy).
and all appear 2-party dominated in the IRV seats (and/or other
seats too). Australia and Ireland are especially revealing
since they are not 2-party dominated in non-IRV seats.
Update: After this page was written, in 2007 Papua New Guinea switched to using IRV in many of its elections. It has not yet developed 2-party domination as of 2013; we shall have to see what the future holds.
Delayed runoff is used in presidential elections in
(where "Q" = qualifies as multiparty country at time of writing)
Brazil Q,
Central African Republic Q,
Chile Q,
Colombia Q,
Congo Q,
Cyprus(meaning the Greek part) Q,
Finland Q,
France Q,
Gabon 1-party-dominated,
Ghana 2-party-dominated,
Iran Q
Liberia Q
Macedonia Q
Mali Q
Mauritania [1party-dominated?],
Moldova [looks to be evolving toward multiparty democracy, but not
totally clear],
Monaco [1-party dominated, but too small to really have parties...],
Nicaragua Q,
Niger Q,
Peru Q,
Poland Q,
Portugal Q,
Romania Q,
Senegal Q,
Slovakia Q,
Uruguay [2 or 3 party dominated, not clear which way].
I have attempted to find out how many of these
countries are not 2-party dominated, i.e. have 3 or more
powerful parties. According to the
Political Handbook of The World 2000-2002 (Binghampton University)
and
http://en.wikipedia.org/wiki/Politics_of_Chile
http://en.wikipedia.org/wiki/Politics_of_Colombia
ditto Gabon, Ghana, Liberia, Mali, Mauritania, Moldova,
Poland, Senegal, Uruguay, and
recent newspapers,
the ones I have labeled Q qualify (anyway, they clearly
are more toward 3-or-more-partyhood than any of the IRV
countries).
Update 2010: "Chile has a multi-party system, within a system with two dominant coalitions. This is because the 1980 constitution approved during the government of Augusto Pinochet made it extremely difficult for marginal parties to achieve electoral success."
– http://en.wikipedia.org/wiki/List_of_political_parties_in_Chile#Current
So, the evidence is not as strong as it could have been, but generally seems to support my hypothesis pretty well.
There may also be some further countries that use top2 runoff. I do not know if my list is exhaustive.
See also:
Reasons why IRV might lead to 2-party domination while TTR tends not to.
Adam Tarr's explanation for why IRV leads to 2-party domination.
More discussion of the differences between IRV and TTR.
Flip rates differ with IRV versus TTR.