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 sample-size 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 two-party vote and lost Missouri with 49.937 percent of the two-party 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:

"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 market-based probability that the Democrats win the presidential election (in the electoral college) is 59, close to 65.

Table 1 gives more details.

Ranking Assumption for 2020 Senate elections

Background The ranking assumption can also be tested using data from the Senate elections. Consier the vote in each state for the Democratic candidate for Senate. Rank the states by the probability that the Democratic candidate wins the state. The ranking assumption says that if the Democrats win state i, they win every state ranked above state i. The ranking assumption can thus be tested by simply looking to see after the fact if the Democrats won a state ranked lower than one they lost (contrary to the ranking assumption). I plan to collect market probabilities 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. Again, the test is a test of the joint hypothesis that the Predictit market probabilities are right and the ranking assumption is right. Data collected from Predictit on September 22, 2020 The current make up of the Senate is 53 Republicans and 47 Democrats, counting the 2 independents as Democrats. Only 16 states are in play in having market probabilities on the Predictit website less than 90 percent and greater than 10 percent. The 16 states ranked by the market probabilities from Predictit for the Democratic candidate are:

state	prob	now
Minnesota	87	D
Colorado	84	R
Arizona	83	R
Michigan	73	D
Maine	73	R	pivot for 50 Democratic seats
North Carolina	65	R	pivot for 51 Democratic seats
Iowa	49	R
Montana	42	R
Georgia, reg.	35	R
South Carolina	30	R
Georgia, spec.	27	R
Arkansas	26	R
Kansas	22	R
Texas	16	R
Alabama	12	R
Kentucky	11	R

57 = Predictit market-based probability of the Democrats controlling the Senate. If the Democrats win North Carolina and all the states above it, they will have 51 seats, counting the 2 independents as Democrats. If they win Maine and all the states above it but lose North Carolina, they will have 50 seats. They will still control the Senate if they win the White House. According to the ranking assumption, the Predictit market probablility that they control the Senate is thus 73 percent (the probablity they win Maine) if they win the White House and 65 percent (the probablility they win North Carolina) if they don't. If we use the Predictit market-based probabilty of 59 percent that the Democrats win the presidential electon, then the ranking assumption probability that the Democrats control the Senate is 0.59x73 + 0.41x65, which is 70 percent. This is noticeably higher than the Predictit market-based probability of the Democrats controlling the Senate of 57 percent. In this case, unlike in the Presidential case, it does not look like the market is using the ranking assumption. Earlier calculations Tests using the 2012 Presidential Election and the 2014 Senate Elections 2012 and 2014 Elections Tests using the 2016 Presidential Election, the 2016 Senate Elections, and the 2018 Senate Elections 2016 and 2018 Elections