PredictIt vs Five Thirty Eight: An explanation of the differences between prediction markets and polling models

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If you’re like me you’ve been looking at FiveThirtyEight and PredictIt election probabilities multiple times a day. Recently I’ve been focusing on some interesting disagreements in electoral outcomes at the state level.  For instance; FiveThirtyEight gives Pennsylvania, Michigan, Florida, Wisconsin and Ohio at least 20% lower probability of a Trump victory than PredictIt.  Why is PredictIt giving Trump a much higher chance in those states? 

One theory is that FiveThirtyEight focuses on polls and who the people of the state will vote for while PredictIt focuses on which candidate will actually win the state. The difference could come down to who is in control of the state. It is possible that the governor or legislature may get to decide who wins. To explore this hypothesis I gathered the current predictions (morning of 2020-11-01) and compared the differences on which party controls which part of the state government (data found here and here). 

Below is a bar chart ranked differences between PredictIt and FiveThirtyEight Trump probabilities on who controls the governor, Upper House, and Lower House. 

One can see that the of the top 10 states with largest discrepancies 6 have Republic Governors, 9 have Republican Upper Legislatures and  8 have Republican Lower Houses.  Interestingly, the states where Predictit has Biden ahead are also generally Republican held.  
To further explore the relationship I made a scatterplot of the difference between Trump probabilities on FiveThirtyEight’s probability below. 

On average Trump gets  ~5.9% higher probability on PredictIt than FiveThirtyEight. Those heavily favored to be Trump states have (less than 15% change of Biden win on FiveThirtyEight) are actually less favored to go for Trump on PredictIt. This is reversed in states that are most likely to go for Biden as Predictit gives them a higher chance for Trump. This could be because prediction markets are not as sure of the polls and expect errors-in-variables from the polls. 
Those heavily favored to be Biden Wins (>80% on FiveThirtyEight) but are held by Republican Upper Legislatures (Minnesota, Wisconsin, Michigan, and Pennsylvania) have an average difference in prediction probabilities of 22% while those that are Democratic held have a ~5% difference. If FiveThirtyEight correctly estimates the voting intention and PredictIt correctly estimates who wins the state then this implies ~a 15% chance that legislatures can decide the outcome in these states. 

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