Ranking Assumption for 2018 Senate elections
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 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 the Senate. Rank the states by the probability on the day of the election that the Democratic candidate wins the state. The ranking assumption says that if the Democratic candidate wins state i, the Democratic candidates will 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 5, 2018. The November 5 data will be used to test the ranking assumption. This 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 13, 2018, 2:30pm EST

According to Real Clear Politics there are 40 Democratic seats that are safe or not in play and 47 Republican seats that are safe or not in play. This leaves 13 states in play. The following are the 13 states ranked by the PredictIt probability that the Democrats win the state.

# D seats state prob
41MN2 85
42WI 85
43NJ 76
44WV 74
45MT 67
46NV 62
47IN 50
48AZ 50
49MO 47
50TN 45
51FL 44pivot for 51 Democratic seats
52TX 39
55ND 38
29 = PredictIt market-based probability of the Democrats controlling the Senate.

If the Democrats win Florida and all the states above it, they will have 51 seats, counting the 2 independents as Democrats, and thus control the Senate. According to the ranking assumption, the PredictIt market probablility that they control the Senate is thus 44 percent (the probablity they win Florida). This is higher than the PredictIt market-based probability of the Democrats controlling the Senate of 29 percent. The market is not quite using the ranking assumption in determining this probability. It probably is reflecting the view that even if the Democrats take Florida they could possbily lose some states above it.