Florida 2000 and Washington 2004

and σ_diff will be given by,

From these we have,

From the manual recount we have,

For which we obtain,

This value of Twill then correspond to the probability that the result measured is statistically insignificant and might just as well have been the result of a coin toss, which can be looked up in a standard "T-Table" for DF and T. Because they are based on "bell curve" distributions like the gaussian function, it's customary to report T-Table results in "one-tailed" or "two-tailed" formats corresponding to either the left/right side of the curve or the entire thing. The former giving the probability of one outcome being more likely than another and the latter giving the probability that any difference between the two at the measured level is random. For our purposes the two-tailed test is more revealing. T-Tables can be found in the back of any standard statistics and probability theory textbook. For T = 0.105 and DF = infinity, this gives,

In other words, there is a 91.5 percent chance that the outcome of the Gregoire-Rossi election was a coin toss. A similar calculation can be run for the final machine tally after recount. Here, Rossi led by a margin of 42 votes and,

From these values we obtain,

This isn't exactly a "mandate" for either candidate!

Chelan County Superior Court Judge John Bridges agreed. On June 7, 2005 he issued his ruling and upheld the Gregoire victory. In a 52-minute statement he rejected nearly every claim made by Rossi and the WSRP citing their inability to provide "clear and convincing" evidence. He also pointed out that even if the standard of proof were lowered to a "preponderance" of evidence only, they would still have lost. That evening Rossi stated that enough was enough and he would not be appealing the verdict in Washington's Supreme Court, ending the battle.

Turning now to the year 2000 presidential race we may again define similar terms. For the Bush and Gore proportional tallies and the standard errors in Florida and nationwide we have,

and their corresponding T statistics,

The certified year 2000 presidential vote tallies were,

For which equations 2 through 4 and T-Tables give,

But this is only part of the story. As noted, these figures are based on the certified Florida count and reflect the legally mandated machine recount but no disputed votes or manual recounts. Over 175,000 Florida votes were tossed because of irregularities in the handling of ballots or because they were not read by machines. It was later determined that over a third of these were countable by any or all standards county standards for determining voter intent, and nearly 25,000 were clearly countable by even the most lax of those (Nickens, 2001; NORC, 2001). For over a month the Gore campaign fought to have at least a few of these votes considered but the Bush campaign and Florida Secretary of State Katherine Harris successfully blocked the inclusion of all but 342 Gore votes. The Florida Supreme Court eventually ordered Harris to add these, reducing the final margin to 195 votes bringing the final values to,