Should You Vote? And How?

This post is a discussion of the U.S. voting system and the implications for strategic voting. The general conclusions are:

  • You should vote if the election is competitive
  • You should spend time researching candidates in competitive elections
  • In competitive elections, identified differences in policies between major party candidates makes it worth voting for a major party and not a third party
  • This includes smaller elections, but may not include voting for president as many states are uncompetitive

Soon I will be discussing in depth specific presidential candidates, but this post does not contain any endorsements and instead contains all the other information you might want to consider before actually researching and ranking candidates.

There’s a lot of extensive calculations doing the cost-benefit analysis, so it may be more interesting to skip around to the sections you find most interesting.

Why Do We Vote?

Harder and Krosnick (2008) suggest a variety of reasons people vote, some of which take into account cost-benefit analysis elements like the ease of registering to vote, strong differences in preferences of candidates, and the closeness of elections. They also identify many other qualities associated with voting which seem to be unrelated to the actual election, like voter demographics (education level, age, race, marital status), feelings of duty, and civic organization membership.

Generally speaking, I think most people vote by trying to select the “best” candidate through their personal lens, and they often ignore strategic voting. In contrast, I would like to cautiously advocate thinking about voting more in terms of a cost-benefit or “rational” approach.

I think voting analysis should be done in a more rigorous, forward-looking way because this approach forces a much deeper interaction with the democratic system (and the problems inherent with it). If we keep our interaction with the system relatively shallow and devoid of analysis, we can’t fix major problems that govern the voting rules themselves. It can also lead to tribalism and groupthink when actual solutions require significant problem solving and nuance.

I was inspired to think about this recently when a friend asked who I planned to cast my presidential vote for, especially since I’ve talked about third parties in the past. I responded that I hadn’t thought much about who I’d personally vote for, since I live in an extremely uncompetitive state. She surprisingly disregarded this point, and asked more pointedly who I was going to vote for. The implication seemed to largely be tribal signalling; what mattered is that we’re all on the right side, not whether our actions are actually effective.

I think this way of viewing the political system is relatively common and generally bad. Everyone has nuanced views shaped by their perspective, experience, background, etc. We should strive to create a political system with robust voting (like approval voting or score voting!) that is able to capture lots of information from voters, instead of what it currently does which is allow many ballots to be purely signalling.

However, in this blog post, I’ll be taking our troubled electoral system as is, and assume that I am unlikely to change it today, or to convince many other people to change their thinking about the electoral system. Given what we know about how ballots will be cast, what should I (and my relatively small base of readers) do to strategically maximize the payoffs in this nationwide election?

Should you vote at all?

I detailed a lot of issues with the American electoral system in the last post: uncompetitive elections, bad voting systems, gerrymandering, etc. Given all of that, whether to vote at all is an important question! Voting requires time and effort, time that could be spent in other ways that improve the world. Many libertarians don’t vote, pointing out that the chances of your vote deciding an election are minuscule. But this excellent paper (Edlin, Gelman, Kaplan 2007) makes a rigorous case for why they should.

The “waste of time” argument can be compared to arguments against playing the lottery. Yes, the payoffs if you were to cast the deciding vote in a tied election are huge, just like winning the lottery could be life-changing. Yet, you are unlikely to win the lottery. Edlin et al take this argument head on, modeling it using this equation:

Net Utility = pB - c

  • Utility is the term we’re using to describe whether voting is worth it
  • p is the probability of changing the election outcome
  • B is the benefit from voting
  • c is the cost of voting

Basically, if the benefit of deciding the election (i.e. winning the lottery) times the chance of changing the election (the election is tied until you vote) is higher than the cost of voting, we should vote. Unfortunately, p is absurdly small. It’s proportional to the total number of voters, and it’s not uncommon for many of our elections to include hundreds of thousands, if not millions of voters. There’s also the issue that many elections are uncompetitive. Thus this modified equation from the paper:

Net Utility = \frac{K}{n}B - c

  • n is the total number of voters
  • K is based on the closeness of the election (it’s the inverse of the expected percentage margin of victory). It reflects what fraction of the vote is actually “swing voters”.

More on K, for most competitive elections where we expect our candidate to get between 45-55% of the vote, K would be about 10. It is inverse to how close we expect the spread to be, so if polling indicates the candidates are within the margin of error (the closest possible election we could measure), we expect K to peak at around 25 (indicating a 4% margin of error). As elections become more of a blowout, K trends towards 1. But even if the election is close, and you estimate thousands of dollars difference in payoff between the candidates, the number of voters, n is a major problem as it quickly erases any chance of you actually affecting the outcome. Note if you add in the benefits of your family or future children, it’s not going to help much as this number is fixed and small, while the total number of voters is often in the millions.

Ok, so now the good news: the paper points out that the vast majority of voters care about what happens to the country, not just themselves. It is true that for voters completely uninterested in everyone else’s well-being, there is no reason to vote in most cases. But if you take into account the wider social benefits, then voting is often beneficial:

Net Utility = \frac{KN}{n}\alpha b - c

Here, we’ve exchanged capital B for Nɑb, where:

  • B was the total benefit
  • b is the benefit per person
  • ɑ is the amount you discount others’ benefits compared to your own
  • N is the total population of the jurisdiction of the election

N is usually a lot larger than the actual number of voters n, but the ratio of N/n depends on the jurisdiction versus the voters. For a gubernatorial election, it’s probably ~2.5, but for a congressional election, N is the whole country, while n is only your state or district. This is looking pretty good now.

There’s not much guidance of ɑ since it’s really up to the person, although the paper uses an example of ɑ = 0.1. How valuable is it to you that random strangers are $100 better off? Most people give some to charity and so clearly ɑ is something, but intuitively it doesn’t seem to be 1 since that would imply you’re indifferent between keeping all your money and giving it to a stranger. Sometimes there are “matching” charity drives, but those don’t necessarily seem more successful than regular charity, so that might imply ɑ < 0.5. The the rest of this post, we’ll use 0.1 and K=10, since those seem like reasonable assumptions and so that these terms will cancel out. Feel free to recalculate with your own values.

The Close Elections Assumption

Close elections are doing a lot of heavy lifting in this model. For the remainder of the post, I’ll be assuming that the election being discussed is close, but I should note, this actually isn’t that common. Most incumbents are handily reelected, and 34 states are at 90% or higher to vote for one presidential candidate or another a couple months before the election. There are a variety of ways to check if an individual election is actually close, and this should always be the first step before even checking out the costs and benefits of an election. They include prediction markets like PredictIt or Betfair. We’ll discuss the electoral college more directly, including swing states, later in this post, but larger elections for senator and governor might have prediction markets which can tell you when to expect a blowout. For House races, there are some prediction markets for very competitive races, but another good resource is the Cook Political Report which categorizes House races as “solid”, “likely”, “leans”, and “tossups”.

Resources for local elections for state legislature are harder to come by. Historical data can be helpful to lookup an incumbent, but sometimes this information just isn’t available. If anyone has any good advice on how to gather information for local elections, please send it to me on Twitter or leave a comment. I would love to expand this section.

K means we still shouldn’t vote in blowout elections, N/n we will address at each election, and now we just need to calculate b and c.

Costs

This isn’t straightforward, but we can estimate the cost c based on a few variables, resulting in a range for most people from an hour to a few hours. If we take the median U.S. wage of ~$20, that’s $20-$60, although since I would hope that my readership would have really high time valuations (OTOH the length of this post clearly indicates I have too much free time), that might push this range more like $50-$150. This cost of voting includes the time and effort to register to vote, research the candidates, and fill out the ballot.

Registration time costs can vary wildly. You might already be registered as most DMVs will ask if you want to register while you’re there. But if you’ve moved since your last DMV visit, you often have to fill out a form and mail it in. Finding the forms, filling it out, mailing it, etc is going to cost some time, although if you don’t move again before the next election, you can split that cost across several election cycles. If you don’t have an ID at all because you don’t drive, your state might require an entire trip to the DMV (although voter ID laws vary). I’d estimate such a situation would likely triple the cost of just voting and research time. Next, research is essential if we are going to count the social benefits b towards reasons we should vote. Obviously, we all approach politics with our own biases and viewpoints. However, I think I can still advocate for a systematic approach, trying to find the issues that have the broadest impact on the world and then comparing the candidates on those specific issues. Voting itself doesn’t take too long especially if you can request an absentee ballot which I would have recommended even before the pandemic.

Candidate research has challenges; it can be difficult to track down candidate positions. If candidates haven’t held office before, they have no record to look up, and you’re left sifting through their vague campaign websites, tweets, or speeches. You could rely on party affiliation, but that may not map well onto issues you care about. Even if you do generally prefer generic Republicans over Democrats or vice versa, a cursory lookup of each candidate is vital, as you never know when an extremist or controversial candidate could slip by, trying to ride party affiliation to office.

National or statewide races tend to be less costly in research terms since you might already be somewhat familiar with the candidates and any differences they have, so I would expect this model to support voting in more prominent races more unambiguously. This is a change from how I thought about voting in the past.

For the rest of the post, I’m going to use $300 as the cost for voting because it seems likely to be far higher than the actual cost for most people; if we can show voting (in close elections) makes sense at this cost, we’ll have shown it for the vast majority of readers.

Net Utility = \frac{KN}{n}\alpha b - 300

Benefits

That covers the costs of voting, what about the payoffs? The bottom line is that the government in the U.S. is pretty large. With a fiscal budget of trillions of dollars, even small changes can have large payoffs. This means that for most (competitive) federal elections, it’s almost always worth it to vote. State officials depend on the state budget and impact of state laws, but they too are often worth voting in.

There is, of course, uncertainty in this model. For single executive positions like President and Governor, we can be reasonably sure of policy differences which we might be able to quantify. For example, Trump has significantly reduced legal immigration into the country, while Biden has opposed this move. Legal immigrants are quite likely to start businesses and pay taxes, and so the order of magnitude difference in benefits from this Biden policy over Trump is at least in the tens of billions of dollars. Of course, immigrants can start major companies that have huge impacts on the country, like Google, eBay, and Tesla. These second order effects start to complicate how long it takes us to research candidates and compare across many issues, and with the higher research costs, the higher the benefits have to be to justify all this work.

So we’ve got uncertainty in how well we can quantify any specific policy issue, but we also are uncertain about which policies will be important; most people didn’t know terrorism was going to be presidential issue a year after the 2000 election, nor pandemics four years after the 2016 election.

Nonetheless, the following sections explore best estimates we can make about prospective candidates and incumbents to see if voting is worth the effort, given some reasonable assumptions. Moreover, with the cost of voting we calculated of $300, we only have to believe there is a difference in payoff between candidates of a few hundred dollars per capita for voting to be clearly worth it. These sections are pretty dense showing the work, so feel free to read as much or as little as seems interesting before moving on to the section about uncompetitive elections.

Governor

We can reach the $300 threshold most simply for gubernatorial elections. As stated earlier, to calculate the benefits side of the equation we can cancel out K and ɑ, leaving us N*b/n. Gubernatorial elections are simpler because N is the population of the state and n is the number of voters of a state (in e.g. Senate elections N is the whole county while n depends on each state so the ratio varies widely). The ratio of population to voters is between two and three for governor races, so I’m calling it 2.5. With c=$300, dividing that by 2.5 yields b>$120 for Net Utility to be positive. Meaning we only have to see a difference of $120 in expected per capita benefit between gubernatorial candidates for it to make sense to vote (and probably that’s too high).

Net Utility = 2.5b - 300
0 < 2.5b - 300
300 < 2.5b
120 < b

Can we do that? Here is a list of U.S. states with their accompanying budgets, including per capita budgets. $120 per capita is lower than 6% of the budget of all states. I suspect different governors can result in 6% of the budget going to different places. Additionally, state governments also pass plenty of non-fiscal legislation which won’t show up on our budgetary calculations, but is likely a major part of whatever gubernatorial candidates run on. I’d argue that reaching a $120 per person difference in expected outcomes between two candidates is pretty doable if the election is competitive.

Finally, note that similar logic applies to all state officials that run in statewide races.

House

For legislative elections, uncertainty becomes much worse, as there is additional complications introduced when legislators are part of a much larger body.

If we take the cost of voting as conservatively high at $300, then we just need the benefits of voting to be higher than that, even if figuring out the actual benefits is hard. Again this is down to Nb/n. N here is the whole country, so it’s easier to combine it with b to create the full benefit for the whole country of one House candidate winning over the other. That’s what we’re trying to find out. n is the number of voters in a House district. It varies, but is usually between 200,000 and 400,000. Worst case scenario is 400,000. In this worst case then, Nb, the total benefit of a candidate winning has to be greater than $120 million.

Net Utility = \frac{1}{400,000}Nb - 300
0 < \frac{1}{400,000}Nb - 300
300 < \frac{1}{400,000}Nb
120,000,000 < Nb

Can we convince ourselves that a House seat is worth more than that? I think we can do a clever lower bound estimate on how valuable a House seat is by looking at single-margin House votes over a two year period since that’s the length of a term.

Thinking through this problem: half the time a close vote goes the way you want, and half the time it doesn’t. Additionally, ties count as failures to pass, so changing a two-vote bill passage to a tie counts as a flip, but a two-vote defeated bill that turns into a tie is still defeated. You can take a look at my data and script here, but it’s not an exact science. I’m not checking whether these votes are actual final passage, discussions of House rules, rules of debate, or even if it’s actually a 3/5 vote that just happens to fail with a tie. In fact, the data source I’m using called voteview seems to have some inaccurate data compared to the House website, so any conclusions we take should be ballpark estimates. Nonetheless, since 1991, I find we would only expect a flipped House seat to change a couple votes a year. In a two year term, we’ll call it one to four votes. Maybe there are a few more that are simply not seen in this data set, but I would be surprised if there were more than say…10 per term.

So what does this mean? The sheer size of the federal budget means even small changes can have large payoffs; even a hundredth of a percent of the federal budget would be hundreds of millions of dollars. Individual legislators can submit amendments to fiscal bills which could change a hundredth of a percent of the budget. But since the amendments process is strongly controlled by House leadership, it’s hard to say how much power there really is at the individual legislator level. There are also non-fiscal bills whose fate is much more in the balance; a single failed vote could mean they never pass at all (examples might include Obamacare or free trade agreements).

Essentially, this is a fat-tailed scenario (the average is dominated by outliers). Most of the time, I’d guess your representative doesn’t cast deciding votes, and those deciding votes aren’t on interesting things. But every once in a while, they likely stick in an amendment or pass a bill that has a massively outsized impact that far exceeds the $120 million threshold. Still, I should admit that this is tricky .

Obviously, if the House majority were in the balance, that would pretty quickly explode the benefits of a House election, as your vote for your representative would contribute to your preferred party holding the House, assuming you prefer one party over the other. For full calculations, check Footnote 1, but it would significantly outweigh the costs discussed if the House were in the balance (this year it appears it is not).

There’s a lot of uncertainty. Quantification of policies is hazy at best, and it’s also very difficult to predict individual candidate’s actual votes or which votes will actually happen. I think future research in this area should explore situations where important issues are entirely ignored by candidates (or by Congress), as reasoning here is hard. Nonetheless, important policy differences likely exist and so it makes sense to undertake the cost of researching candidates in close House elections.

Related: I would really appreciate a website that lists every close vote so voters can look up their representative and see (A) if these votes were important and (B) whether they agree with the way in which their representative voted.

I am least confident in this section’s calculations, but assuming risk aversion of outlier scenarios (or the House being in the balance), I think we’ve gathered enough evidence that the better candidate winning would result in more than $120 million dollar difference.

Senate

Similar “close votes” logic can be applied to the Senate, although it’s complicated with the Vice President who can break ties. You can see some of the methodology discussion in Footnote 2.

Again, the methodology is rough, and I haven’t been able to count cloture votes which are often important, as well the fact that we are overcounting actual close votes, since some of these are listed as 51-49 when in reality they were cloture votes which needed 60 ayes and they weren’t close at all. I count something like ~6 votes flipped per year if you flip a Senate seat. At 6 year terms, that’s ~36 votes flipped per election, but again, this is an overestimate of close votes, but an underestimate of cloture votes. At best this gives us an order of magnitude estimate. There is another source of uncertainty when senators vote against their party, which I found slightly more common in the Senate than the House, so keep that in mind as well (538 has some data on that here).

Looking up close votes, it’s clear they vary a lot in importance. The latest roll call vote I could actually find that was a single vote victory (roll call 51) was an amendment adding boilerplate language to the joint resolution to prevent the US from attacking Iran without congressional authorization. Flipping this vote seems like it’d have no impact on anyone’s life. Roll call 30 is much more interesting. In it, 47 democrats, Susan Collins, and Mitt Romney voted to subpoena John Bolton for the senate trial of the president. The vote failed as 51 Republicans voted against it. Here, clearly an additional democratic vote would have been large in revealing whatever John Bolton would have said, although likely would have remained far short of the 67 votes needed to remove him from office.

Generally speaking, I think we can say there are more close votes in the Senate due to being a smaller chamber and having six year terms instead of two. Additionally the Senate also has more responsibility in major appointments. I estimate 4-10x as many close votes and more important votes. However, the number of voters in a Senate race varies massively since districts are not population adjusted like in the House. For example, the 2018 California Senate election had 11 million votes, while the Wyoming Senate election had only 200,000, basically equivalent to a House district. Of course, we should note that the Wyoming Senate election wasn’t close and the California senate seat wasn’t that close either, and even then it was between two Democrats so the difference in payoff was likely smaller than between a Republican and Democrat. Here’s a worst case scenario for Senate benefits in California. Again, were looking for Nb as that’s the benefit to the entire country of a Senate seat flipping:

Net Utility = \frac{1}{11,000,000}Nb - 300
0 < \frac{1}{11,000,000}Nb - 300
300 < \frac{1}{11,000,000}Nb
3,300,000,000 < Nb

That’s $3.3 billion. Can we find that in close Senate votes over six years? I think so. Unlike highly variable and rare House votes, we can usually guarantee at least one close vote will happen on an important topic. $3.3billion is less than a percent of non-military discretionary spending, so this seems plausible.

Our conclusions are similar to the House elections. In close elections, it makes a lot of sense to vote even though there is going to be a lot of uncertainty in what votes elected officials will actually face and even what their position could be. Voters in smaller states with close Senate elections have the largest expected payoffs. If you’re uncertain about which candidate is better because of previously mentioned issues with candidates ignoring your primary issues or split among important ones, close Senate elections in small states are probably worth the time to sit down and try and do some estimations of each candidate and policy payoffs.

The Electoral College

I wrote about the implications of the electoral college for third parties in 2016. This year’s post on strategic voting is an elaboration on that model, so even though I’ve taken a slightly different editorial position, the implications for president are similar. It all comes down to the K variable we’ve been using. I’ve had to preface every recommendation with the fact that the election must be close, because even Edlin at al don’t say there’s a positive payoff to vote if the election is already decided.

This most often asserts itself in the presidential election with the electoral college. The way to think about this idea is the “Tipping Point Jurisdiction”. If we listed every state in order by (Trump percentage) – (Biden percentage), and then added up the number of electoral votes, the state that puts either one above 270 is the tipping point. In 2016, this was Wisconsin. Even though Michigan was closer in percentage points, Clinton would have needed to win Michigan, Pennsylvania, and then Wisconsin to get 270 electoral votes. In 2000, this was famously Florida. Your vote for president is only decisive if cast in the Tipping Point Jurisdiction.

Here is a prediction market for chances of any state becoming the Tipping Point state. Because of PredictIt’s fee structure, these probabilities are slightly inflated, and I wouldn’t trust much in a market below 5% to reflect what bettors actually thought. Additionally, it’s still relatively early in the election cycle, so we’d expect more certainty as we get closer to election day.

StatePredict It %538 %
PA2323
FL2224
WI1410.4
MN88.9
MI86.4
AZ75.3
NC63.7
NV42.8
OH32.7
Total: 9587.2

This isn’t meant to be a projection, but just a snapshot that we can use. Even today, two months before the election we’re 90% sure that one of these states will be the tipping point state. The payoff equation for these swing states is pretty clear:

Net Utility = \frac{Nb}{n}p_tp_m - c
  • Nb is again going to be the full benefit to the country (actually, I guess the world?) if one candidate is president compared to another.
  • n is the number of voters in your swing state
  • pt is going to be the chance your state is the tipping point jurisdiction, which is what table above shows
  • pm is the probability that the margin of the electoral college ends up being less than the electoral votes in your state.

These ideas are taken from this paper by Gelman, Silver, and Edlin. To get a rough estimate, we can use this prediction market, which suggests for most states pm is probably only 10-20%, although that could change as we get closer to election. We probably need a full table of probabilities, but here’s Florida’s calculations:

Net Utility = \frac{Nb}{9,500,000}0.22*0.17 - 300
0 < \frac{Nb}{9,500,000}0.22*0.17 - 300
300 < \frac{Nb}{9,500,000}0.0374
2,850,000,000 < 0.0374Nb
76,203,000,000 < Nb

So if there’s a difference in the world of Biden being president over Trump of $76 billion, it’d be worth it to vote in Florida, although it’d be good to redo the calculations with updated numbers closer to election day. Can we get to that number by comparing Biden and Trump? I think so, but you’ll have to wait until my next blog post for the full discussion.

Additional Offices

I don’t have much to add here because advice becomes exceedingly hard to give. The math suggests that state legislator elections will actually scale marginally well since you have a much smaller pool of voters and thus your vote is worth more, precisely outweighing the loss of stakes when switching from federal to state elections. You can try to do the same trick I did earlier with small vote margins in state legislatures, and I’d be curious what you find. Many states are dominated by one party and so I can imagine fewer close votes, but I don’t know. However, as mentioned earlier, the costs to obtain good information might be much harder. Single office elections like Mayor seem much more likely to be easier to calculate benefits and compare candidates.

But What If It’s Not Close?

The short answer is: don’t worry about uncompetitive elections.

The longer answer is: there might be a couple marginal reasons to vote. For example, in presidential elections, ballot access for third parties often depends on small thresholds for third party votes, like 2% or 5%. These might be achievable if you prefer third parties and live in a non-swing state. This is likely what I will personally do, as I live in an uncompetitive state, and tend to favor libertarian candidates.

Also, a quick note on personal enjoyment; some people really like voting. I’ve eschewed psychological reasoning in the rest of this post, but we can’t ignore that a sense of duty or tribal fervor could also be a benefit you get that outweighs the cost of waiting in line or filling out registration forms. The reason I only include those benefits in this section is that unlike benefits from policy, these psychological benefits do not accrue to your fellow citizens. In close elections what should motivate our actions is what would actually improve the world.

When it comes to Donald Trump, there have been predictions and accusation by Obama and Trump of election engineering that could occur during this election. This is concerning. If you strongly support or oppose Donald Trump, it may be worth it to vote even in uncompetitive states to push the popular vote total in your direction in the hopes of making the vote such a rout that a constitutional crisis is impossible. I’m unsure to what extent this will matter in the case of a contested election compared to election results in swing states, but The Economist thinks a decisive popular vote could assure an uneventful transition of power. In swing states, I recommend voting for a major party anyway.

Third Parties in Close Elections

In perhaps a disappointment for my libertarian skewing readership, it only makes sense to vote for third parties in elections that aren’t close. For good or bad, there are tons of uncompetitive elections, and I think third parties, and the Libertarian Party in particular should continue to target those elections. In gerrymandered districts where single party rule dominates, they have a chance to become a real “second party”. The payoff of who is in government is actually really high, and so on expectation, it makes sense to choose a specific major party candidates when both have a chance to win.

That doesn’t mean you can’t advocate for voting reform (reminder that approval voting is on the ballot in St. Louis this year!), or call your senator, or donate money to libertarian causes, it just means that some elections matter and you can have real impact by deciding the winner.

Footnotes

Footnote 1: House majority calculations. If you see strong differences between Nancy Pelosi and Kevin McCarthy deciding which legislation is brought to the floor, that could potentially be worth tens of billions of dollars, maybe even $100 billion. I’m doubtful it would be worth much more than that though, as this is only one chamber of one branch of government. And of course, if you’re a libertarian who disagrees with much of what both Nancy Pelosi and Kevin McCarthy believe, then such differences in majority control are smaller. The analysis here would be like a second order election on top of your vote for local congressman. Assuming House majority control is in the balance in the election (this year, it doesn’t appear to be), you’d need to add another term to our equations to account for smaller probability of your representative casting the deciding vote for Speaker. We’d thus multiply by an additional K/n where K=10 and n=435 for all House members.

Net Utility = \frac{KN}{n}\alpha b\frac{K_H}{n_H} - c

We’ll cancel out K and α, Nb is the full benefit of a certain party being in control, n= between 200,000-400,000 for most House districts. The second fraction KH/nH = 0.023. Overall, this works out to ~$5000 ballpark estimate for a $50B difference in majority control. Obviously, this would make it worth it to vote in House elections, although again, that’s not likely to be on the table in this election.

Footnote 2: Senate calculations. The Vice president acts like an extra Senator. So if the VP is someone you agree with, you can take that into account (or vice versa). But if there’s uncertainty (for example, we don’t know who will be Vice President in 2021), you can estimate that half the time the VP votes in your interests. The other half of the time your “side”, however you define that, loses the vote. An extra senator would flip those votes because the tie would be broken before the VP votes (i.e. the VP could break a tie against your side if it’s 50-50, but doesn’t get a chance to if the vote is 51-49). I downloaded Senate vote data here and looked at votes from 1991 on. You can find my code and data here.

Picture credit: League of Women Voters of California, licensed under CC-BY-2.0