I already said this in a comment at an earlier thread, but it is the sort of thing that is at the very core of Fruits & Votes, and hence deserves its own space…
By my calculation, the effective number of vote-winning parties in Costa Rica’s 2 Feb. election was 6.21. The effective number of presidential candidates was 4.36. Both easily break the record for the country’s elections back to 1953. The old averages and maximums were 3.21 and 4.84 for vote-winning legislative parties and 2.37 and 3.30 for presidential candidates. (Historical figures based on Bormann and Golder’s dataset.)
Costa Rica’s party system sure is unrecognizable from what it was for so long!
The effective number of parties or candidates is by now the most well established measure of electoral or legislative fragmentation. It is simply a weighted count of the number of components (parties, candidates, or anything else) where the components are weighted by their own size through squaring them. Operationally: square each component’s share (out of 1), sum the squares, and take the reciprocal of the sum. Originally proposed by Laakso and Taagepera in a 1979 article.