Background
The ranking assumption can be tested using data from the Senate elections. Consider 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). The following is my final ranking before the election on November 8. I have used three betting markets and 538 to examine the sensitivity to the choice of markets. (538 is not a political betting market. The probabilities are what the 538 website thinks they are.) Earlier calculations using the 538 and Predictit probabilities are in Earlier Data for Senate 2022.
Data collected at 7:30pm on November 7, 2022
The make up of the Senate in 2022 is 50 Republicans and 50 Democrats, counting the 2 independents as Democrats. At most 11 states are in play in having probabilities that are not essentially zero or one. The 11 states ranked by the Predictit probabilities for the Democratic candidate are:Probability | ||||||
state | now | Predictit | Smarkets | Betfair | 538 | |
Colorado | D | 90 | 87.72 | 87.3 | 92 | |
New Hampshire | D | 64 | 72.46 | 69.7 | 72 | |
Arizona | D | 53 | 56.50 | 57.5 | 66 | |
Pennsylvania | R | 43 | 42.37 | 38.2 | 44 | pivot Betfair and 538 |
Georgia | D | 39 | 40.00 | 40.0 | 37 | pivot Predictit and Smarkets |
Nevada | D | 37 | 37.04 | 33.5 | 49 | |
Wisconsin | R | 13 | 15.15 | x | 19 | |
Ohio | R | 11 | 9.52 | x | 13 | |
North Carolina | R | 9 | 12.20 | x | 18 | |
Florida | R | 3 | 4.00 | x | 5 | |
Utah | R | 2 | 5.00 | x | 4 | |
.. | ||||||
Dem. control | D | 33 | 34.48 | 32.1 | 42 | betting contract or simulations |
Dem. control | D | 39 | 40.00 | 38.2 | 44 | ranking assumption |
The Betfair probabilities are the average of the bid and ask. An x means the bid-ask spread was too large to be sensible. "Dem. control" is the probability that the Democrats get at least 50 seats. For the three betting markets there is a separate contract for this. The 538 probability is based on 40,000 simulations using probability distributions for each state.
The ranking assumption probabilities of Dem. control are computed as follows. The pivot state using the Predictit and Smarkets ranking is Georgia. If the Democrats win Georgia and all the states above it, but none of the states below it, they will have 50 seats, counting the 2 independents as Democrats. The ranking assumption thus implies that the probability of the Democrats controlling the Senate is the probability that they win Georgia, which is 39 percent using Predictit and 40.00 using Smarkets. These compare to the betting market probabilities of 33 and 34.48 respectively.
Betfair has Georgia ahead of Pennsylvania, so Pennsylvania is the pivot state, which has a prabability of 38.2 percent. This compares to 32.1 percent for the betting market probability. 538 has Nevada ahead of both Pennsylvania and Georgia, which also leads to Pennslvania being the pivot state, which has a probability of 44 percent. This compares to the 538 probability of the Democrats controlling the Senate of 42 percent.