Princeton Election Consortium

Innovations in democracy since 2004

Outcome: Biden 306 EV (D+1.2% from toss-up), Senate 50 D (D+1.0%)
Nov 3 polls: Biden 342 EV (D+5.3%), Senate 50-55 D (D+3.9%), House control D+4.6%
Moneyball states: President AZ NE-2 NV, Senate MT ME AK, Legislatures KS TX NC

New PEC feature: Redistricting Moneyball 2020

July 30th, 2020, 7:31pm by Sam Wang

(Watch our explainer video here.)

The main campaign stories in 2020 are the Presidential election and the fight for control of Congress (mostly, the U.S. Senate). But lurking beneath those high-profile questions are state legislative elections, which will set the political playing field, including Congressional districting, for the next 10 years.

State legislatures determine policies that will affect millions of Americans. In addition, this year they decide who will draw the maps of U.S. Congressional and state legislative districts after the 2020 Census. Their reach will last a decade, unlike the presidency (4 years) and Senate seats (6 years).

The Princeton Election Consortium has designed a model to identify races where voters have the most leverage to prevent partisan gerrymandering in 2021. A few hundred voters mobilized in the right districts can bring about bipartisan control of redistricting, and get fairer districts for a decade. Our findings are in the PEC Moneyball map. (Later we will add other important state races, including U.S. Senate and state ballot questions.)

Our calculations will help you direct your efforts as you decide where to get out the vote and where to donate. At a state and county level, you can take advantage of our calculations using our PEC 2020 ActBlue (for Democrats) and PEC 2020 WinRed (for Republicans).

In this post we describe the methodology used to determine redistricting voter power for state legislative elections. You can also find a more detailed version for election-math geeks here.

We followed a four-step process:

Step 1: In each state, determine which 2020 electoral outcomes would give neither party the power to enact a partisan gerrymander. This is determined by the redistricting protocol set in the state’s constitution. In many states, the two chambers of the state legislature draw the new districts, the governor may veto the plan, and the state legislature can override a veto with a supermajority. As a result, a state will have bipartisan redistricting as long as (1) one party does not control the governorship and both chambers of the state legislature and (2) one party does not have supermajorities in both chambers of the state legislature. Some states have no governor’s veto (e.g. NC), and we adjust the desired electoral outcomes accordingly. We assume that states with an independent redistricting commission (e.g. AZ) will not enact partisan gerrymanders. We focus on congressional gerrymandering and not state legislative gerrymandering, but it turns out that many of the high-leverage states have similar laws for the two processes.

Step 2: In each state, determine the likelihood of an electoral outcome that results in bipartisan control of redistricting. This is not so easy; most forecasts for national elections rely heavily on public polling, but this data is not available for state legislature races. Furthermore, each state has tens or hundreds of small districts, each of which has different candidates and uncertain local dynamics. For this reason, we rely heavily on the race ratings of CNalysis, the only organization that offers comprehensive ratings for individual state legislature races. The group, led by Chaz Nuttycombe, looks at statewide election results in each district, adjusts for the effect of incumbent popularity, researches challengers to assess their quality, goes through campaign finance reports, and predicts demographic trends.

Our model of state legislature elections takes as input the CNalysis race ratings, which consist of a favored party and a confidence level of “Uncontested,” “Safe,” “Lean,” “Tilt,” or “Toss-Up” (no favored party for Toss-Up). We then incorporate results from recent state legislature and presidential elections, which slightly differentiates districts with the same rating. Next, we model uncertainty in the outcome of each race, accounting for the possibility of a uniform shift across the state or among urban/suburban/rural voters. Putting all of this together, we can calculate the probability that the state legislature elections result in bipartisan control over redistricting.

Step 3: In each district in a state, find the amount that a single new vote impacts the bipartisan control probability. We go through every district and run the model from step 2 after adding one to the expected number of votes for a given party. The change in probability gives an estimate of the chances that a given voter in the district will cast the consequential vote for bipartisan redistricting.

Step 4: Quantify the effect across different states. Partisan gerrymandering is more impactful in more populous states, since it affects more seats in U.S. Congress. We estimate that these effects are about proportional to the number of congressional districts minus one, so we multiply the voter powers from step 3 by this number (based on projected 2020 Census results). After normalizing to a 0-100 scale, we get a list of the relative redistricting voter powers to prevent partisan gerrymandering.


Q: If I want to donate money to prevent gerrymandering, which candidates should I give to?

A: This model tells us where votes, not donations, have the highest leverage. These are not necessarily the same thing. There is evidence that political advertising is mostly useful for getting people to pay attention to a candidate, which makes it more effective for first-time candidates than well-known incumbents. Also, a dollar goes farther in a cheap media market and matters more to poorly-funded candidates than well-funded ones. We are not making specific donation recommendations, though we hope interested citizens can use our findings in conjunction with other available information to inform their political involvement in 2020.

In some cases, counties have an unusually high concentration of key districts. Examples include Johnson County, Kansas, and Tarrant County, Texas. At a state and county level, you can take advantage of our calculations using our PEC 2020 ActBlue (for Democrats) and PEC 2020 WinRed (for Republicans).

Q: Why don’t the Toss-Up seats always have the highest voter power in a state?

A: Indeed, the Toss-Up seats are the likeliest to come down to a small number of votes on Election Day. However, if one party is favored to control a state legislative chamber, then the other party will have to do better than expected in order to gain control. This means that they will probably have to win most or all of the Toss-Up seats in order for the chamber to be competitive. If a district is part of almost all of a party’s paths to redistricting power, it is not a high-leverage district. We are not trying to identify the districts most likely to be close, but the districts most likely to be the tipping point for our desired election outcome.

Q: How often will you update this page?

A: Every time CNalysis updates their state legislative ratings, we will re-run the model. They do updates about once a month. We may run the model weekly or bi-weekly between CNalysis updates, though the changes are likely to be small.

Who did the work: Moneyball state legislative model, Jacob Wachspress and Connor Moffatt. Map interactive, Hope Johnson. Site administration, Mike Hallee and Indraneel Purohit.

Tags: 2020 Election · Moneyball · Politics · Redistricting

11 Comments so far ↓

  • A New Jersey Farmer

    Looks like NJ is off to a fast start on this one. As you said in a previous post, voters will get to say if redistricting gets delayed.

  • Vote for democracy

    I’m sorry sir, but the GOP has shown itself to be an authoritarian cult from Trump all the way down to the supporters across the country. To suggest we give them “bipartisan” control of anything is dangerous. Across the country they are fighting Dem Governors to stop fundamental voting rights.
    The GOP has shown us who they are and they must go the way of the Whigs.

  • Karl Chwe

    The map doesn’t seem to work for me. I can see a few colored districts, but clicking on them does nothing. Also the orange buttons don’t do anything. Does the map require javascript or flash?

    • Sam Wang

      To my knowledge no. It’s Mapbox, a common platform. Help us diagnose this? Write to Mike Hallee, who is mdhallee at princeton dott edu ?

    • Mike Hallee

      Thank you for alerting us of this. The map does require your browser has javascript enabled. Could you email me at with more details like what browser and device you were using, and any other issues you noticed? We want to make sure everyone can access this information, so we always appreciate bringing bugs to our attention.

  • David Elk

    Hi Prof. Wang,

    Thank you for this tool, it is fascinating. I know you’re not giving specific donation advice, but I’m curious: do you think it’s better to focus on a few races to concentrate efforts, or spread across the board? I don’t have a billion dollars, and I keep fighting with myself over this question.

    • Sam Wang

      You may get more satisfaction to adopt a candidate! Personally, I am really into Kansas. Such small races, part-time legislators, so homey.

  • Darren Grant

    In Step 3, what formula do you use to determine the probability of a tied election? I have done some work in / am familiar with that area and so am curious.

    • Sam Wang

      A toss-up’s 50-50. We treat Tilt, Lean, or Safe seats as having larger and larger expected margins for either party, with uncertainty built in. Layered on that are overall swing and uncertainty. In practice, a safe seat is nearly certain to be held by one party.

  • Darren Grant

    Probabilities are inversely proportional to the number of voters? The degree of uncertainty, standard deviation of ultimate winning margin, in percentage points? These are the details I was hoping to learn.

    • Sam Wang

      It’s in the GitHub. Win probabilities, generally speaking in all circumstances, are just the integral of the distributions of probabilities.

      For us, probability is tcdf(margin,stdev,df), where tcdf is a cumulative t-distribution and df is set to 1 or 2 to allow for long-tailed outcomes. Then one has to artfully calculate the margin and standard deviation.

Leave a Comment