## Post-Mortem after the 2020 Senate Election

The discussion below was on the website before the 2020 Senate election. The last data collected was on November 2, 2020. These data are used for the test of the ranking assumption.The Democrats won Georgia, reg., and so according to the ranking below and the ranking assumptionn they should have won all the states ranked above Georgia, reg. They in fact lost North Carolina and Maine, so two errors for the ranking assumption. Predictit made errors regarding Maine, North Carolina, and Georgia, reg.

## 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). Near the end of the 2020 election I collected market probabilities from Predictit on various days, the last day being the day before the election, November 2, 2020. The November 2 data were 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. The earlier calculations are in earlier Predictit data for the 2020 Senate elections.

## Data collected from Predictit at 7pm on November 2, 2020

The make up of the Senate in 2020 was 53 Republicans and 47 Democrats, counting the 2 independents as Democrats. Only 15 states are in play in having market probabilities on the Predictit website less than 90 percent and greater than 10 percent. The 15 states plus Colorado, Mississippi, and Alabama ranked by the market probabilities from Predictit for the Democratic candidate are:state
| prob
| now
| |

Colorado | 91 | R | |

Minnesota | 80 | D | |

Arizona | 79 | R | |

Michigan | 70 | D | |

Maine | 69 | R | |

North Carolina | 60 | R | pivot for 50 Democratic seats |

Georgia, spec. | 52 | R | pivot for 51 Democratic seats |

Georgia, reg. | 42 | R | |

Montana | 34 | R | |

Iowa | 32 | R | |

South Carolina | 25 | R | |

Alaska | 20 | R | |

Kansas | 18 | R | |

Texas | 15 | R | |

Mississippi | 10 | R | |

Alabama | 9 | D | |

64 = Predictit market-based probability of the Democrats controlling the Senate.

If the Democrats win Georgia, spec. and all the states above it, they will have 51 seats, counting the 2 independents as Democrats, and assuming that they lose Alabama. If they win North Carolina and all the states above it but lose Georgia, spec., 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 60 percent (the probablity they win North Carolina) if they win the White House and 52 percent (the probablility they win Georgia, spec.) if they don't. If we use the Predictit market-based probabilty of 64 percent that the Democrats win the presidential electon, then the ranking assumption probability that the Democrats control the Senate is 0.64x60 + 0.36x52, which is 57 percent. This is smaller than the Predictit market-based probability of the Democrats controlling the Senate of 64 percent. So the market is not using the ranking asssumption.