Ranking Assumption for 2018 Senate elections 
PostMortem: November 15, 2018
The Democrats won AZ, and so according to the ranking below and the ranking assumptionn they should have won IN and FL and all states above FL. The won all states above FL, but lost IN and may lose FL. So the ranking assumption made an error regarding IN. PredictIt also made an error regarding IN and maybe FL. 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 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). The market probabilities below are from PredictIt and were collected at 9:00pm EST on November 5, 2018. These 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 regarding the ranking and that the ranking assumption is right. Data collected from PredictIt on November 5, 2018, 9:00pm 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  
41  WI  93  
42  MN2  87  
43  NJ  84  
44  WV  79  
45  MT  66  
46  NV  65  
47  FL  64  
48  IN  53  
49  AZ  48  
50  MO  40  
51  TX  23  pivot for 51 Democratic seats 
52  TN  20  
53  ND  14  
17 = PredictIt marketbased probability of the Democrats controlling the
Senate.
If the Democrats win Texas 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 23 percent (the probablity they win Texas). This is close to the PredictIt marketbased probability of the Democrats controlling the Senate of 17 percent. The market price is thus rougly consistent with the ranking assumption, although a little lower. 