Ranking Assumption for 2020 Presidential election 
Background
The paper, Interpreting the Predictive Uncertainty of Elections, Journal of Politics, April 2009, provides an interpretation of the uncertainty that exists on election morning as to who will win. The interpretation is based on the theory that there are a number of possible conditions of nature than can exist on election day, of which one is drawn. Political betting markets provide a way of trying to estimate this uncertainty. (Polling standard errors do not provide estimates of this type of uncertainty. They estimate samplesize uncertainty, which can be driven close to zero with a large enough sample.) This paper also introduces a "ranking assumption," which puts restrictions on the possible conditions of nature that can exist on election day. Take as an example the vote in each state for the Democratic candidate for president. Rank the states by the probability on the day of the election that the candidate wins the state. The ranking assumption says that if the candidate wins state i, he or she wins every state ranked above state i. Given some ranking, the ranking assumption can be tested by simply looking to see after the fact if the candidate won a state ranked lower than one he or she lost. In the paper the assumption was tested for the 2004 and 2008 presidential elections using Intrade probabilities at 6am Eastern standard time on the day of the election. The test is thus a test of the joint hypothesis that the Intrade probabilities on November 7, 2016, are right and the ranking assumption is right. Using the Intrade probabilities, the ranking assumption was perfect in 2004 and off by one in 2008. In 2008 Missouri was ranked above Indiana, and Obama won Indiana and lost Missouri. Both of these elections were very close. Obama won Indiana with 50.477 percent of the twoparty vote and lost Missouri with 49.937 percent of the twoparty vote. Otherwise, 2008 was perfect. Evidence is also presented in the paper, although this is not a test of the ranking assumption, that Intrade traders used the ranking assumption to price various contracts. 2020 Presidential Election I plan to collect market probabilities by state from Predictit on various days, the last day being the day before the election, November 2, 2020. The November 2 data will be used to test the ranking assumption. The test is a test of the joint hypothesis that the Predictit market probabilities are right and the ranking assumption is right. The data as they are collected are presented in Table 1. Data collected from Predictit on September 22, 2020 On this date, 19 states had market probabilities on the Predictit website less than 90 percent and greater than 10 percent for the Democrats winning the state. The 19 states, ranked by market probabilities for the Democratic candidate, are: 
state  prob  votes  sumvotes  
New Mexico  89  5  200  
Colorado  89  9  209  
Maine not 02  86  3  212  
Nevada  76  6  218  
Minnesota  75  10  228  
Michigan  72  16  244  
New Hampshire  71  4  248  
Wisconsin  66  10  258  
Nebraska 02  65  1  259  
Arizona  65  11  270  pivot 
Pennsylvania  64  20  
Florida  48  29  
North Carolina  47  15  
Maine 02  47  1  
Iowa  36  6  
Ohio  34  18  
Georgia  34  16  
Texas  26  38  
Arkansas  16  6  
59 = Predictit marketbased probability that the Democrats
win the presidential election.
"sumvotes" is the sum of the electoral votes of all the states ranked above the state plus the state's vote. 270 votes are needed to win. You can see that Arizona is the pivot state. If Biden takes Arizona and all the states ranked above it, he gets 270 votes. Of the states ranked below Arizona, he could also win by not taking Arizona, but taking Pennsylvania, Florida, or North Carolina. This would, of course, violate the ranking assumption. There is evidence that traders are more or less using the ranking assumption. According to the ranking assumption, the probability that the Democrats get a majority in the electoral college is the probability that they win the pivot state, Arizona, which is 65. On the Predictit website, the marketbased probability that the Democrats win the presidential election (in the electoral college) is 59, close to 65. Table 1 gives more details.
