Will eventually resolve to the party which won the popular vote for the race, as determined by the local, state, and ultimately federal governments.
In the case the race is called by the major news organizations, the market may optionally resolve early.
This market covers events up to and including Election Day, November 5: if Party A's candidate X wins the popular vote that day, but intervening events cause the next inaugurated Senator to be from Party B, the market will resolve to Party A.
If candidate X switches party affiliations, the switch will not affect the outcome if it is after the beginning of Election Day, local time.
From my latest Manifold newsletter:
Wyoming: Scott Morrow (D) vs. Sen. John Barrasso (R)
Expert forecasts: Solid R (Cook), Safe R (Sabato), Solid R (Inside Elections)
Poll results (538): None
Election result in 2018, a Democratic wave year: R+37 (Barrasso vs. Trauner)
Election result in 2012, amid Obama's reelection: R+54 (Barrasso vs. Chesnut)
Recent Wyoming presidential election results: Trump+43 (2020), Trump+46 (2016), Romney+41 (2012)
Commentary:
Zero polls. In all of the other races, someone — maybe a campaign — bothered to commission at least one poll. But in Wyoming, they know there’s no point.