The Price of a U.S. Senate Seat
Have you ever wondered, “How much does it cost to buy an election?”
Over the summer, I set out to answer this question. I was motivated by the fact that in the 2020 election cycle, Democratic candidates for U.S. Senate raised 1.48 times more than Republican candidates; however, Democratic candidates only won 15 out of 35 Senate races. So I wondered:
- Does campaign money actually impact vote share?
- If so, how much does it cost to buy a 1% vote share?
- How much does it cost to flip election results?
I gathered data from the Federal Election Commission (FEC) for all 35 Senate races in the 2020 cycle. Over $2B was raised across 35 races. TWO BILLIONS DOLLARS! It’s a lot of money, by anyone’s standards. That is equal to 20,000 homes built by Habitat for Humanity or over 270M meals from Meals on Wheels.
Did all that money even make a difference? Turns out, yes it did.
Univariate Analysis
I first set out to establish whether or not there is a relationship between money raised and vote-share. I conducted the following univariate regression:
SenDemVoteShare: Democratic Senate Votes / (Democratic Senate Votes + Republican Senate Votes)
SenDemRaiseShare: Democratic Money Raised / (Democratic Money Raised + Republican Money Raised)
I use shares instead of whole numbers for two reasons. The first reason is to reduce the effect of outliers. If, for example, SenDemRaiseShare was calculated by dividing Democratic money raised by Republican money raised, then if a Republican candidate raised a negligible amount of money, SenDemRaiseShare would be massive. Limiting every value between 0 and 1 eliminates this issue. Second, I do not want my results to be biased by state size or high-profile elections in swing states.
Univariate Findings: My univariate results show a strong, positive relationship between money raised and election results (See Table A at the bottom of this post). My results suggest that for every 1% increase in relative dollars raised, Democrats are expected to win an additional ~ 0.32% of the vote margin (and vice-versa for the Republicans). While the model has a strong Adj. R² of 0.74890, there are likely correlated omitted variables, which I address in my multivariate analysis.
Multivariate Analysis
I next set out to determine if my univariate results hold when additional factors are considered. Multivariate analysis can also help determine whether a specific source of funds (for example, individual money or PAC money) is more impactful in terms of “buying” election results. I conducted the following multivariable regression:
SenDemVoteShare: Democratic Senate Votes / (Democratic Senate Votes + Republican Senate Votes)
SenDemRaiseShare: Democratic Money Raised / (Democratic Money Raised + Republican Money Raised)
PresDemVoteShare: Democratic Presidential Votes / (Democratic Presidential Votes + Republican Presidential Votes)
OpenSeat: 0 if the candidate is running for re-election, otherwise 1
Grassroots: (Individual Democratic Money Raised / Total Democratic Money Raised) / ((Individual Democratic Money Raised / Total Democratic Money Raised) + (Individual Republican Money Raised / Total Republican Money Raised))
Individuals: # In-State Democratic Donors / (# In-State Democratic Donors + # In-State Republican Donors)
PAC: (Democratic PAC Money Raised / Total Democratic Money Raised) / ((Democratic PAC Money Raised / Total Democratic Money Raised) + (Republican PAC Money Raised / Total Republican Money Raised))
Multivariate Findings: My multivariate model is a stronger overall model than my univariate model, as the Adj. R² increases from 0.74890 in my univariate model to 0.94892 in my multivariate model. Not surprisingly, the strongest predictor of how a state voted in the 2020 U.S. Senate election is how it voted in the 2020 presidential election (see PresDemVoteShare). However, even after accounting for states’ 2020 presidential vote, Senate vote share can still be increased with additional funds. With a t-statistic of 4.2674, SenDemRaiseShare is still a positive and significant variable in predicting how a state will vote in its Senate election, suggesting that a 1% increase in raise share results in a ~.12% increase in vote share.
The only other significant variable in my model is the share of individual in-state donors. If a candidate has more in-state donors, they can reasonably expect their party to increase in its vote share. Although neither PAC share nor Grassroots prove statistically significant, it is worth noting that the coefficient for PAC is larger than that of Grassroots, showing that, in a way, getting PAC money “goes further” than increasing grassroots support. The last variable I examine, OpenSeat, has no effect on either party, possibly because it has equal impact across the aisle.
The Price of an Additional 1% Vote Share
Below I have summarized my findings regarding the prices of an additional vote share, including the dollar amounts of money raised per candidate (from FEC website) as well as my calculation of SenDemRaiseShare:
(If you want to see my math regarding how the right two columns are calculated, scroll down to the “Math” section of this post.)
As you can see from the data above, the price of an additional 1% vote share is not cheap. From the Democratic perspective, the cheapest pickup would have been an additional 1% vote share in Wyoming for $400,438, while the most expensive pickup would have been an additional 1% vote share in Georgia’s regular election for $70,733,745. From the Republican perspective, the cheapest pickup would have been an additional 1% vote share in Rhode Island for $380,770, while the most expensive pickup would have been an additional 1% vote share in Tennessee for $175,284,769.
The price for 1% of the vote share for one party is not the same as the price of 1% vote share for the other party for any given race because my model takes into consideration how much one candidate already raised relative to the other candidate. Since my model uses raise share, equal to Democratic Money Raised / (Democratic Money Raised + Republican Money Raised), if the Democrats had raised a very small amount of money compared to the Republicans, doubling their small amount of money would double the numerator but keep the denominator roughly the same, thus almost doubling the raise share. However, if Democrats had raised a very large amount of money compared to the Republicans, if they double their large amount of money the denominator will only be a little bit larger than the numerator both before and after the doubling. Note this math works in reverse for Republicans since Democratic Money Raised / (Democratic Money Raised + Republican Money Raised) = 1- (Republican Money Raised /(Democratic Money Raised + Republican Money Raised). Overall, the more money one party has already raised, the harder it is for that party to increase their raise share, and thus the harder it is to increase their popular vote share.
Another result of this non-linearity is that my model forecasts nine candidates (three Republican candidates and six Democratic candidates), representing 12.9% of the candidates in my study, are not able to buy an additional vote share. Due to the non-linear nature of my model, for more politically extreme states where the dominant party claims a very large raise share, my model does not generate a rational price for an additional vote share.
Taking a closer look at the nine candidates unable to purchase an additional vote-share, we see these candidates all dramatically outspend their rivals in states where their party is dominant, thereby fully saturating the market.
The Price To Flip Election Results
Once I determined the price of a single vote share, I set out to determine the cost of flipping election results. Because the way I calculate raise share [Democratic Money Raised / (Democratic Money Raised + Republican Money Raised)] is not a linear function, neither is any calculation including raise share. Thus, in order to determine the price to reach 50% of the vote share, you cannot simply take the price of an additional 1% and multiply it by the number of additional points needed to win. Instead, you must divide the desired change in the popular vote share by 0.11743 (the coefficient on SenDemRaiseShare) and then set that equal to Democratic Money Raised / (Democratic Money Raised + Republican Money Raised). If you want to find Democratic Money Raised, you must make Republican Money Raised a constant, and vice versa. Finally, you can solve the equation by cross multiplying and then subtracting the money that was actually raised to determine how much more money would have been needed to win a 50% vote margin.
My model predicts that 16 out of the 35 Senate races, 45.7% of the Senate elections, could have been bought for the following prices:
Similar to my model’s limitation predicting prices when raise shares are disproportionally high in a state with a pervasive political persuasion, my model predicts that certain elections could not have been bought. In the calculation involving flipping a result, the Senate vote share also comes into play. In order for a race to be “for sale” the race itself must be close in terms of vote share, in addition to having a close raise share.
Of the 16 races which could have been purchased, Republicans could have purchased 12 Senate seats (for a total of $801,656,972) while Democrats could have purchased four Senate seats (for a total of $7,960,051,130). Prices range from $8,178,714 for the Republicans to purchase the New Mexico U.S. Senate seat, to $7,555,151,641 for the Democrats to purchase the South Carolina U.S. Senate seat.
Math
The benefits of using shares instead of absolute values is to enhance the model’s predictive capabilities by reducing (a) outliners and (b) variability due to state size and high-profile elections. However, using shares instead of absolute values reduces the intuitiveness of my findings. Below I provide an example of how I calculated an additional 1% of the vote share in the Michigan 2020 Senate race, as well as how I calculated the price of flipping the Michigan 2020 Senate election results from blue to red.
How much would it have cost Democrats to increase their vote share in the 2020 Senate election in Michigan by an additional 1%?
How much would it have cost Republicans to increase their vote share in the 2020 Senate election in Michigan by an additional 1%?
How much would it have cost to flip the 2020 Senate election results in Michigan from blue to red?
Summary
For those of you who have pondered the price of a federal election, I hope this post proves meaningful. My research provides quantifiable evidence that money does indeed influence election outcomes on the federal level. Campaign money goes disproportionately further in terms of buying vote shares when a campaign has previously raised less money. This disincentivizes raising additional money in close races, which incentives each party to match, but not exceed the amount raised by the other side. These data also show where money should have been spent more effectively in Senate races during the 2020 election cycle. Democrats should have spent more in North Carolina, since it is the state that would have been “cheapest” to flip, and the Republicans should have spent more in New Mexico for the same reason.
