I thought that this was pretty common knowledge, especially after the result of the 2000 election, but given some of the sentiments flying about recently and diaries like this, I thought that a diary explaining why it would be ridiculous for Hillary Clinton to run as an independent and why it would not be a good idea to vote for Nader unless you honestly had no preference between the two candidates put forth by the Republican and Democratic Parties.
The main reason that we have two political parties is because of our voting system, single-member district plurality (SMDP). SMDP is structured such that for a given electoral division (district), there is one winner (single-member) who is decided by earning the most votes for that area (plurality).
FactCheck.org published a brief explanation as part of their Ask FactCheck series
The reasons here are mainly statistical. Third parties may have statistically significant support (maybe 15 percent of voters in every district supports a third party). But in an SMDP system, the third party may well not win any seats. So those voters will likely join with another party and look for a compromise candidate that could represent them. Similarly, suppose that a district has 200,000 conservative voters and 110,000 liberal voters. One would expect a conservative candidate to be elected. But if two conservative parties each run a candidate, then a liberal candidate may well be elected – unless the conservative parties unite behind a single candidate.
But, one might argue, it isn't always the case that a third party or independent candidate loses. For instance take the example of the 2006 U.S. Senate race where incumbent Senator Joe Lieberman (who we all know and love) defeated both the Democratic nominee, Ned Lamont, and the Republican nominee, Alan Schlesinger. However, Presidential races are even more biased against third parties because of the electoral college.
In the election of every other major office, governors, senators, representatives, etc., there is only one "district" which is contested and thus the winner is the one who gets the highest popular vote in that district. But in the Presidency, there are multiple weighted districts that determine the winnner. In most cases, these districts are states (with the exception of the District of Columbia). States are allowed to apportion delegates as they wish, with most choose to give their entire delegation to the candidate who wins the plurality in their state.
This system thus magnifies the effect described by FactCheck.org by raising the actual votes for a candidate away from individual voters to the state delegations. Thus a third party candidate needs to actually win pluralities in enough states to constitute a majority of the delegates, which is an even more daunting task than winning a single district, because of the diverse terraine and the fact that a second place finish in any district with winner-take-all apportionment (most states), second place is no different than third, fourth, or fifth place. One cannot simply have a widespread support but also support that is concentrated enough in enough states to win.
There are a couple historical examples of significant third parties disrupting elections that really illustrate that point. The first and most recent example is of course, the 2000 election. Here is a map of the results courtesy of the nationalatlas.gov. The coloration may be confusing, since Bush is blue and Gore is red:
As one can see by this official count, Gore lost the electoral vote to Bush. While this may have been different if the Supreme Court had not stopped the recount in Florida, it would have certainly been different if all Nader voters had instead voted for Gore, which besides giving him the claim of majority support would have added Florida and New Hampshire to his state count. This is true even if you take all voters for other third party candidates (Buchanan, etc.) and add them to Bush's total, yielding a map that looks like this:
The electoral vote would have been Gore 295 Bush 242 and we would have President Gore in the White House right now (assuming re-election).
An even more striking example is the 1912 election, when Woodrow Wilson won the electoral vote by a landslide against incumbent President William Howard Taft and former President Theodore Roosevelt:
For a bit of background, both Taft and Roosevelt had competed in the Republican primary, with Taft winning. However, instead of dropping out, Roosevelt ran on the Progressive Party ticket. The infighting among the Republicans greatly helped Wilson, who despite only getting 41.8% of the popular vote to the 27.4% of Roosevelt and the 23.2% of Taft (for a combined total of 50.4% of the vote), won 435 electoral votes to Roosevelt's 88 and Taft's 8. The funny thing is that if you combine the votes for the two "Republicans", Wilson loses decisively:
Republican 420 Wilson 111
Granted, perhaps some Taft voters would have voted for Wilson over Roosevelt or vice versa, but the point stands. If Roosevelt had been the Republican nominee or if he hadn't continued to run after losing the nomination, Woodrow Wilson would never have been President of the United States.
And that is likely what would happen if Clinton ran as an independent. President McCain would sit in the Oval Office a year from now, which is why she won't run (and why Obama wouldn't she were to somehow win the nomination). Nader, on the other hand, should be harmless as long as voters, especially voters in swing states, treat him as the irrelevant candidate he is. All in all though, this stands as a warning against voting for a third party candidate. Until this system gets the overhaul it badly deserves, voting for third party candidates is at best symbolic unless there has been some serious political tumult that has damaged the either of two parties sufficiently for a third to take over, which doesn't seem likely.