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 October 20, 2020 On this date, 20 states had market probabilities on the Predictit website less than 90 percent and greater than 10 percent for the Democrats winning the state. The 20 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  88  3  212  
New Hampshire  78  4  216  
Nebraska 02  77  1  217  
Minnesota  76  10  227  
Nevada  74  6  233  
Wisconsin  68  10  243  
Pennsylvania  68  20  263  
Michigan  67  16  279  pivot 
Arizona  58  11  
North Carolina  52  15  
Florida  51  29  
Maine 02  42  1  
Georgia  41  16  
Ohio  36  18  
Iowa  33  6  
Texas  29  38  
Arkansas  15  6  
South Carolina  11  9  
64 = 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 Michigan is the pivot state. If Biden takes Michigan and all the states ranked above it, he gets 279 votes. Of the states ranked below Michigan, he could also win by not taking Michigan, but taking Arizona, where he is favored. This would, of course, violate 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, Michigan, which is 67. On the Predictit website, the marketbased probability that the Democrats win the presidential election (in the electoral college) is 64, close to 67. So the market participants are roughly using the ranking assumption. Table 1 gives more details.
