It is interesting to compare Socialist parties in the USA, with their equivalents in other countries. In Spain, the Socialists won the election and took control of the government (2004). In France (2006), supposedly the Socialist candidate Segolene Royal is currently regarded as the most likely to win the presidency. [Later note: she unexpectedly lost to N.Sarkozy.] In the USA, there are several socialist parties, all of them generally getting tiny fractions of 1% of the vote.
Why the huge difference? Is it really the case that USA voters are so immensely less socialist in their hearts than French and Spanish voters?
We don't think so. Sure, we are willing to believe in a factor of 2 or 3 more socialism in French and Spanish hearts. But not a factor over 1000.
The real difference is that in France, elections for president are conducted with the top-2 runoff system, which is a system that does not cause long-term decline and death of third parties. (The USA's plurality system, and Australia's Instant Runoff system, do cause such decline and death.) In Spain, elections are done via a party-list proportional representation system, which again is one in which third parties are capable of surviving and flourishing.
But it gets worse. In the USA, there is not just one big Socialist Party. No. There are numerous tiny socialist parties, most or all of which appear (based on speaking to their members) to hate each other – although they would appear to be similar based on examining their platforms. These include the Socialist Party of the USA, Socialist Workers Party, Socialist Equality Party, Labor Party, Socialist Labor Party, and the Socialist Action Party. Such fratricidal enmity does not seem to exist (at last not to nearly as large a degree) in France and Spain.
Why is that?
Each mini-party has to fight with its siblings for the tiny share of the USA vote-pie consisting of socialist voters. If we had range voting or some other clone-immune voting system, no such fratricidal fight would exist and there would be no such thing as a "share of the vote pie" and no such thing as "vote splitting." Problem solved.