What exactly is wrong with partisan gerrymandering?

When I tell people I’m a political philosopher, the response is usually either “So how ‘bout that guy in the White House?” or bewilderment. I’ve never come up with a good, pithy explanation of what political philosophy is, but fortunately this recent paper on partisan gerrymandering will make matters much easier.

Charles Beitz’s article “How is Partisan Gerrymandering Unfair?” is a great example of public philosophy. He takes an issue on which many people have strong opinions, carefully examine the issue, and see whether the opinion holds up to scrutiny or needs revision. Often this exercise involves figuring out what exactly is the issue at stake. If people think the problem with gerrymandering is x, but when you look carefully they actually have a problem with y, then the philosopher has done a valuable service. And indeed that’s what the paper does.

“Partisan” gerrymandering, of course, involves manipulating the boundaries of legislative districts in a representative body for partisan advantage. How is this possible? First, voters’ partisan affiliations (say, Red and Blue) often correlate with geography. This means that co-partisans will tend to cluster together — for example, voters in cities tend to vote for Blue. Second, assume that legislative districts in a legislature must be a) spatially continuous and b) have the same population. B) means that the legislature satisfies the “one person, one vote” (OPOV) condition, assuming for the sake of argument that everyone in each district is eligible to vote. Third, the number of possible legislative districts that satisfy a) and b) will almost certainly be n > 1. Given the first condition, it’s possible that certain maps satisfying a) and b) will be more favorable to one party or the other. If one party controls the redistricting process, they can select an eligible map that secures them more seats in the legislature.

This figure illustrates the possibility for partisan gerrymandering in drawing district lines nicely. Note that all maps satisfy the continuity and OPOV requirements. However, we also have to keep in mind that this figure assumes a certain voting rule: each voter votes for a single candidate, and the candidate with the most votes is elected to the legislature. The first clause means a single-member district (SMD) and the second clause is known as “first past the post” (FPTP).

In map 3), gerrymandering works by “packing” Blue voters into the two U-shaped districts on the map — the Blue candidate wins by overwhelming margins in both districts — and “cracking” Red voters between three districts (“cracking” and “packing” are the two basic techniques of gerrymandering). In contrast, map 2) spreads out or “cracks” the Blue voters between all five districts, which allows Blue to win all the races. 2) also shows how a gerrymander can occur with “compact” district shapes, or shapes that don’t look like bizarre artifacts of a computer program. Roughly, “compactness” means that for any two points a district’s border, you can draw a line connecting those points that is entirely within the district border. This is a useful corrective to the thought that “normal” district maps could eliminate gerrymandering.

3) also illustrates the importance of the SMD/FPTP voting rule for gerrymandering. Because of the voting rule, most of the Blue voters packed into the two U-shaped districts are “wasted”— assuming 100% turnout and no ties, seven of nine Blue voters cast ballots that are not necessary for their (single) candidate to win. However, wasted ballots are also consistent with a “fair” district map such as 1) where, with the same assumptions, nine of ten voters in each district “waste” their votes.

Finally, note how a district map’s effect on parties needn’t result from anyone’s intentional choice. Even if we suppose 1–3 are the only eligible maps, a random choice among the three would still result in a map that advantaged either Blue or Red.

So that’s the phenomenon of partisan gerrymandering. Why is it bad? As the article notes, many people feel partisan gerrymandering is wrong because it means that the votes of some citizens are “wasted” or “diluted” — it makes some citizens’ votes more important than others. Another related objection is that it reverses the desired direction of control in a representative democracy — partisan gerrymandering allows representatives to select their voters, when it is voters who should select representatives.

However, there are some problems with both these reactions. Specifically, there are three puzzles for explaining why partisan gerrymandering is bad:

1. The first puzzle is the fact that a district map can produce the same effects as a deliberate partisan gerrymander by accident. Note that how I described the possibility of partisan gerrymandering above is fully consistent with random selection among the eligible district maps. As I said above, it’s mistake to assume that a partisan gerrymander can only result from an intentional choice. Rather, gerrymandering arises from both the fact that there are many district maps satisfying OPOV and continuity and the correlation between party affiliation and geography. The puzzle, as the article puts it, is this: “if the objection to partisan gerrymandering has to do with its distorting effect on the representation of the people in the legislature, why should we care whether the distortion is produced intentionally or as a by-product of acting for a nonpartisan aim in constituting the system?” (328)
2. The second puzzle has to do with how gerrymandering “dilutes” the power of some voters. One natural interpretation of “dilution” is that gerrymandering violates OPOV — one person’s vote in her district might have the same influence on the outcome as multiple votes in another district. But as the example and picture above illustrates, gerrymandering can occur with a legislative map that satisfies OPOV. Moreover, as the article shows, gerrymandering can also occur when district maps must satisfy further conditions, such as compactness (roughly, a line connecting any two points on the district’s border must not pass outside the district border — the center map satisfies compactness while the right map doesn’t) and historical/geographic fit (e.g. county lines). Given this, in what sense does partisan gerrymandering treat voters unequally, and why is that a problem?
3. The final puzzle is that in a SMD/FPTP voting system, each voter only elects a candidate in her legislative district. Voters (ideally) consider which candidate will represent them and cast their ballot accordingly. But the problem with gerrymandering is allegedly that partisan bias appears at the level of the jurisdiction as a whole between the total votes received for each party and its seats in the legislature. The puzzle is that there is no jurisdiction-wide electoral contest between parties — only a set of separate contests each in a single district. It is not clear then why partisan bias at the level of the jurisdiction is actually a problem rather than just the result of a bunch of separate legislative contests.

One natural response to these puzzles (especially 1) and 3)) is that partisans who gerrymander are exploiting knowledge about the spatial distribution of voters to advance their own interests. Perhaps their intention in gerrymandering violates some duty to voters to advance the common welfare rather than their own or their party’s interest. The problem with this response is that while such an bad intention is sufficient to make partisan gerrymandering wrong, it is not necessary as the possibility of an “accidental gerrymander” shows. A further problem is that it presupposes a standard for an (un)acceptable district map. However, this standard would have to assume some view about the substantive conditions an acceptable district map must satisfy (e.g. OPOV). A purely procedural standard, such as, “A district map must not be justified only by its partisan advantages,” would rule out too few district maps. As we saw above, a district map could satisfy non-partisan conditions like compactness and OPOV while still producing a gerrymander.

What we need, then, is a standard for an acceptable district map. Much of the reporting on gerrymandering, including the Wonkblog graphic I shared above, implicitly assumes a proportionality standard — a party’s share of seats in the legislature should reflect its jurisdiction-wide vote share. If the jurisdiction is 60/40 Red/Blue, then the legislature should be 60/40 Red/Blue. Unfortunately, this criticism is overly broad — electoral systems with SMD almost never satisfy this standard. In electoral systems with SMD, a 1% increase in total (jurisdiction-wide) vote share almost always translates to a >1% increase in seat share in the legislature. By contrast, proportionality requires that a 1:1 ratio between vote and seat share.

Another possible standard is partisan symmetry. Assume a two-party system (which as I explain below is the case for an electoral system with SMD). An electoral system satisfies this standard if and only if, given that the Red Party won 45 seats with 53% of the vote, and the Blue Party won 37 seats with 47% of the vote, the Red Party would have won 37 seats with 47% of the vote and the Blue Party 45 seats with 53% of the vote. In other words, if the parties had switched their vote shares, they would have switched their numbers in the legislature as well (note that this is a weaker condition from proportionality). The partisan symmetry standard might explain why we think gerrymandering “dilutes” votes for one party by translating votes for one party into more seats than the same vote for the other.

However, we have to keep in mind the distinction between the district-level and jurisdiction-level here. As Beitz shows partisan symmetry can also occur at the jurisdiction level without any deliberate gerrymander. This is again a feature of SMD — if representatives are chosen by geographically discrete districts, voter movement between districts can change the distribution of seats in the legislature without changing the overall vote shares. All this is consistent with partisan symmetry within each district. What this shows, then, is that partisan asymmetry can occur no voter in an election is treated unequally toward the election’s outcome.

Another reason why partisan asymmetry might be bad is that it allows a party to win a majority of seats in the legislature even when another party commands a majority of total votes in the jurisdiction. This again seems like a promising version of the objection. However, as we saw with puzzle 3), there is no jurisdiction-wide election under SMD. Because there is no jurisdiction-wide election, voters in a jurisdiction-wide election are not given more influence depending on the candidate they support. Instead, voters contend in a set of independent elections within districts. And because the nature of the parties, candidates, and campaigns would be different under a jurisdiction-wide election, there is a fallacy of composition in assuming that the total vote share of each party under SMD is what a jurisdiction-wide election without SMD would have produced. Because party systems are endogenous* to the electoral rules, there would be different parties and different candidates if the electoral rules allowed for a single jurisdiction-wide election without SMD. So we cannot use the total vote shares of parties to make an argument that voters for one party have been treated unfairly.

(*In political science, Duverger’s Law says that the number of parties in an electoral system is equal to n + 1, where n is the number of representatives elected to a district. So a system like the U.S. with SMD produces two parties.)

There is a problem, then, with objecting to gerrymanders on grounds that they treat individual voters unfairly or give some voters more influence than others. However, Beitz suggests a different way to make sense of the dilution objection.

Let’s distinguish between a vote that’s decisive and a vote that’s successful. A decisive vote is one that turns a losing candidate/issue into a winning one — it is non-wasted. A successful vote is a vote for the winning candidate/issue, even if the vote is not decisive (a successful vote could be wasted). Decisiveness and success generate different measures of how “powerful” a vote is in an election. I’ll call these power(d) and power(s). Another factor affecting a vote’s power, however, is the distribution of political preferences among voters in the election. Power(d) is the fraction of total voting “profiles” (how everyone else votes), weighted by the probability of each profile, in which her vote is decisive. Power(s) is the fraction, etc., in which her vote is successful.

The key point here is that when political preferences correlate with geography, voters will differ in their power(s) and power(d) depending on their district. Consider map 3) above:

1. Within the U-shaped districts (call any of them District B), each Blue voter has more power(d) and power(s) than any Red voter in District B. Within the districts won by Red (call any of them District R), each Red voter has more power(d) and power(s) than any Blue voter in District R.
2. If we compare Blue voters between districts, Blue voters in district B have less power(d) and more power(s) than Blue voters in District R. Red voters in District B have less power(d) and less power(s) than Red voters in District R.

By this we have the following table (± just means that we cannot compare using this purely ordinal method):

Power(d): Red,District-R > Blue,District-R > Blue,District-B > Red,District-B

Power(s): Red,District-R ± Blue,District-B > Red,District-B ± Blue,District-R

Recalling that there are more District-R (3) than District-B (2) in map 3), we can see intuitively that Red votes across the entire jurisdiction of 50 people are more powerful(s) and powerful(d) than Blue votes. However, Map 3) does not make all Red voters more powerful — in particular, it makes Red voters in District-B, where they are a tiny minority, less powerful than some or all Blue voters, depending on your measure of voting power. It also makes some Blue voters more powerful than other Blue and Red voter. This example shows that the effect on voting power from gerrymandering is actually more diverse than commonly appreciated.

What this example shows is that gerrymandering exploits the existence of geographically defined legislative districts to reduce the voting power of some and increasing it of others. However, inequalities in voting power are almost inevitable in an SMD system, except in very rare cases. This means that under SMD, voters are less likely to have a candidate who closely approximates their own political preferences. Beitz argues (correctly, I think) that this is an inevitable cost of SMD FPTP in exchange for a more effective and disciplined legislative process. Unlike in PR systems, in which the legislative agenda comes together after elections occur, an SMD FPTP system starts with organized parties that propose a legislative agenda and select candidates accordingly before an election. The advantages of this approach to agenda formation that the majority party can effectively and stably govern. The downside is that representatives and the party agenda will on the whole be farther from voters’ policy priorities.

Beitz thinks this suggests an answer to the puzzles 1) and 2) above. If divergence between the voter’s preferences and their representatives is an inevitable cost of SMD, partisan gerrymandering “induce[s] inequalities in the distribution of this cost that cannot be justified as necessary to achieve the benefits of SMD. On this view, the effect of partisan gerrymandering is to impose an unjustifiably large share of the costs of SMD on those whom it disadvantages” (345). In response to puzzle 2), then, gerrymandering does not compromise political equality or treat voters unequally so much as concentrate the cost of a voting system on voters for one party rather than another. Gerrymandering is a feature of a voting system that cannot be justified by the aims of that voting system. Moreover, this response suggests a standard for district maps (roughly, “minimize expected differences in voting power”) that explains why “accidental gerrymandering” might be objectionable as well as intentional gerrymandering.

What about puzzle 3)? Beitz argues, in brief, that because the effect of gerrymandering is to reduce the probability of a partisan candidate’s election in certain districts, the jurisdiction-level partisan bias is has an indirect effect on voters. If voters vote for candidates of a party at the district level for instrumental reasons, such as to realize that party’s legislative program, then a gerrymander indirectly and unjustifiably reduces the opportunity of some voters to bring about their legislative preferences. In particular, their opportunities have been reduced in such a way that cannot be justified by the advantages of the voting system. The role of parties in connecting voters with legislation, then, explains how partisan bias at the jurisdiction-level can be objectionable even with only district-level elections.

This paper is going to become my go-to example of how political philosophy can be relevant to contemporary political problems. Careful reflection upon and analysis of our political judgments can perhaps help members of the public see the questions before them more clearly.