Nate Silver and his FiveThirtyEight site has achieved significant notoriety for developing a system to carefully aggregate election polls to create well-calibrated statistical forecasts of outcome elections; his site publishes daily updates to predictions for primary and general elections in House, Senate and Presidential races.

Prediction markets have offered an alternative to poll aggregation in forecasting elections. Markets such as (the now defunct) InTrade, the Iowa Electronic Markets, PredictIt, and others ask users to buy and sell shares assigned to each candidate in each race, so that the price point corresponds to the probability of victory. In this question we focus on PredictIt, which allows users to place relatively small real-money bets on candidates.

Both FiveThirtyEight and PredictIt have published probabilities for each state in the 2020 Presidential Election.

Which forecasts will prove to be more accurate?

*Will 538 outperform PredictIt forecasting the 2020 Presidential Elections?*

To compare, we will score each set of predictions using a Brier score averaged over all N=51 races, computed as

where enumerates the possible outcomes (i.e. possible winners) in the th race out of N, where is the forecast probability of candidate winning the th race, and is assigned 1 if candidate wins the th race, and 0 otherwise.

For example, if PredictIt assigned 52% to Trump and 48% to Biden in Texas and if Trump won then PredictIt would achieve a Brier Score of

A lower Brier score is better, with perfect predictions corresponding to S=0.

This question resolves positively if the Brier score for the 51 races is lower for 538's probabilities than for PredictIt's probabilities, where we will take values as of 1400 UTC on 02-Nov-2020, and election outcomes as reported over the coming days.

To obtain the PredictIt probabilities, we will download the market data from here ; take the average of the prices for each contract (ie (bestSellYesCost + bestBuyYesCost + (1-bestSellNoCost) + (1-bestBuyNoCost))/4) ; and convert to probabilities as Dem_Probability = Dem_Price / (Dem_Price + Rep_Price).

To obtain the 538 probabilities we will download the CSV from here and take the winstate_inc for Republicans and winstate_chal for Democrats in each state. (Ignoring congressional district specific probabilities)