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Candidates for the presidential election of the US collect donations in relation to their campaigns.

Candidates are sometimes compared based on the total amount of donations they received.

But what do the numbers actually mean to a candidate?

I see aspects of the campaign that are affected by the availability of money in a simple way. There are expensive technical resources that are expected to increase the rating of the candidate. For example air time in TV, number of print ads.

These seem to scale linearly: Double the money results in a doubled effect. Spending 1000 $ more increases the return by a known estimate.

With this, the candidates compete on a simple, brute force resource based competition. If that is all there is to campaign donations, it makes sense to compare candidates by total amount of donations received, because their probability to win are dependent on the amount in a simple way.

Apart from that, there are other aspects of received donations, and I would like to understand their relevance:

  • The total amount of donations is correlated to popularity, and therefore, a high amount demonstrates high popularity to the public.

  • Thee candidates compete on limited resources that are available only to one or few highest bidders. For example, there may be known best advertising agencies.

  • Available cash allows for general flexibility. But is this relevant?

  • The number of campaign events could be limited by available money, but I would assume it is typically by available candidate time.

  • Donations could support providing transport and accommodation to large numbers of supporters to travel to campaign events - is that used?

Are some of these, or any other aspects of campaign donation totals relevant?

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I would say that in the case of donations, you need to look not at the total dollar value a candidate generates, but at the number of smaller donations generated, to better gauge support. If two candidates are generating $1 million dollars each, but Candidate A has gotten that from a majority of larger donors, while B generates from smaller donors, it's reasonable to say B is a more popular candidate as people who can't afford big donations are donating en mass.

As pointed out, it's a good gauge, but the Presidency is not a straight popularity contest, so it should be taken with a grain of salt. That said, the Electoral College has only diverged from the popular vote in 5 races in the 200+ history of the nation.

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There is quite a bit of research out there on campaign spending. Much of it is normative or legal in nature, but there is some good quantitative stuff out there.

Short story: Spending is important. Especially for challengers running against an incumbent.

Money is Good

In a simple sense, spending more is associated with winning more. Abramowitz (APSR, 1988) explored multiple effects on Senate elections in the United States. He tested both cases where an incumbent was running against a new challenger, and open seat elections. It's tough to express their findings in terms of dollars because they adjust the dollar-value of campaigns to reflect both the size of the state and inflation. However, according to their statistical tables it appears that challenger's spending is far more useful for predicting the incumbent's success than the incumbent's spending is!

Writing about Irish elections, Benoit and Marsh (Party Politics, 2003) summarized the relationship visually: enter image description here

The same result is reflected in the chart from Benoit and Marsh. The line for incumbent spending is fairly flat: there is little marginal benefit to spending if you are an incumbent. on the other hand, the marginal benefits for incumbents can be pretty significant! The effect on the incumbent should be clear - if the challenger can significantly increase their chances of winning based on spending, then that means the incumbent's odds have decreased.

There is also some research about the source of funds. Confirming the importance of campaign spending, Alexander (Political Research Quarterly, 2005) finds that spending one's own funds (self-financing) actually decreases the odds of winning, while PAC spending increases it.

But what about everything else?

The studies above show that there is some relationship between spending and electoral success. But what about all the other factors?

The Abramowitz article cited above tests 16 potential causes. After adjusting for the other 15 factors, a 1 pt. change in incumbent spending results in a 1.31% increase in votes for the incumbent. On the other hand, the presence of a celebrity challenger reduces the incumbent's votes by almost 6%, an incumbent scandal reduces changes by about 7%, concerns about the incumbent's health can reduce their votes by 8%, etc. Spending has a significant effect, but it is not the only - or even the most important - effect.

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  • You are overly positive about this. In particular, this ignores the possibility that challengers who win are particularly popular. And that popularity leads both to winning and to high fundraising (which leads to high spending). That explanation is entirely consistent with incumbent spending having little effect while challenger spending does. And it also explains why self-financed spending does not help, as it doesn't derive from the root variable (candidate popularity?) that drives both fundraising and winning. If spending were itself helpful, we'd expect self-financed spending to work.
    – Brythan
    Aug 16, 2019 at 4:21
  • @Brythan It does not ignore that effect at all, but I didn't cover it in the short summary I posted. It's in the literature, though. Some of the articles try to control for other notions of extant electoral support.
    – indigochild
    Aug 16, 2019 at 4:23
  • @Brythan Sorry, I wrote that response forgetting that most of the internet likely doesn't have access to some of these articles. I'll add something in to my answer to cover that. It's a good point.
    – indigochild
    Aug 16, 2019 at 4:37
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These seem to scale linearly: Double the money results in a doubled effect. Spending 1000 $ more increases the return by a known estimate.

This is not necessarily true. While it is true that election donations and votes tend to scale together, they don't always. And it is quite possible that the relation is not causative. I.e. it is quite possible that campaign spending doesn't cause more votes. The alternative explanation is that both campaign donations and votes come from attraction to the candidate. So better candidates get more donations and more votes, even though more donations do not cause more votes.

This explanation better explains results like Donald Trump winning over Hillary Clinton. He was unusually popular with poorer people and she was unusually popular with richer people. She received considerably more in donations than he did but lost the electoral college (she did win a plurality of the popular vote).

In terms of campaign rallies, there is some actual data on that from Sabato's Crystal Ball. Campaign rallies slightly helped the candidates. But in both cases, the effect was smaller than the standard error, so not statistically significant.

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