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On gerrymandering
Most people of my acquaintance agree these days that drawing district lines to lock in partisan advantage is dirty pool, anti-democratic, counterproductive, and un-American. And there are plenty of data, and plenty of smart mathematical minds, to find better solutions. But how would you define a "better" solution?
A frequently quoted statistic: in 2016, Republicans won 49% of all the votes for House of Representatives seats in the country, but they won 57% of the seats in the House of Representatives. This is obviously wrong, but how is it wrong? Intuitively, we'd like to know that a party that gets n% of the votes should get roughly n% of the seats. (Most districting systems don't even aspire to that, but aim for "quasi-proportionality" in that the percentage of seats should be a "reasonably smooth" increasing function of the percentage of votes.)
Let's call that the Proportionality Criterion.
The recent Pennsylvania gerrymandering case was brought by Democratic voters in (I think) every district in the state, and their complaint was that their votes (and thus, in a sense, their free speech) had been devalued in advance by putting most of them into districts where their votes would make no difference: either they were "cracked" into districts that were foreordained to go Republican, or they were "packed" into 90%-Democratic districts where one more Democratic vote would make no difference. The plaintiffs claimed that most Republican voters had a much greater opportunity to affect an election. Intuitively, we'd like everybody, regardless of party or race or religion or dwelling-place, to have an equal voice in elections, in the sense that everybody has a roughly equal likelihood of affecting the outcome. To a first approximation, let's say this "likelihood" is inversely proportional to how far from 50% the vote total is in your district; if PV is the proportion of votes in a district, add up 1/(k+abs(PV-.5)) over all districts that go Yellow and see whether it's substantially different from the sum over districts that go Pink. (The "k" is a small positive constant introduced to prevent infinite results.) Call this the Equal Voice Criterion.
Of course, one can meet the Equal Voice Criterion by making every seat "safe" for one party or another, because nobody (of either party) is in a competitive district. We've seen the effect of such districting plans: candidates are more worried about party primaries than general elections, so they are dragged to the extremes of their respective parties, and we get a dysfunctional legislative body incapable of compromise. So equality of voices isn't enough: we also want to maximize total "voice", perhaps by adding up 1/(k+abs(PV-.5)) over each district regardless of who wins it. Call this the Maximal Voice Criterion.
This is maximized when PV is the same for all districts, i.e every district roughly reflects the political breakdown of the state as a whole (for a fanciful example, assign districts by the last few digits of Social Security number rather than by home address). This is probably a TERRIBLE idea: in a state with 55% Yellow voters and 45% Pink voters, it produces a 100% Yellow legislature (or Congressional delegation or whatever).
There's been a lot of talk lately about the Efficiency Gap Criterion: roughly, if the number of "wasted" votes (any vote for a losing candidate, and any vote over 50% for a winning candidate) is substantially different between parties, it suggests that somebody's cheating on behalf of one party over the other. This one is very similar to the Equal Voice Criterion, and it's equally problematic.
As pointed out in Chambers, Miller, and Sobel, the efficiency gap has a false-positive problem: in a hypothetical 100% Yellow state, there is no districting system that would produce other than a 100% Yellow legislature. Since it is impossible to gerrymander this state, any reasonable measure should find it un-gerrymandered, but the efficiency-gap measure finds a 50% efficiency gap in favor of the Pinks. (One wonders how they managed to manipulate the districting process so effectively without a single Pink in the state, much less in the legislature.) As it happens, a heavily-gerrymandered map in which the Pinks win every district by a single vote also has a 50% efficiency gap in favor of the Pinks, and the efficiency-gap criterion makes no distinction between these two opposite-extreme scenarios.
Those authors also point out that an efficiency gap of zero can often be achieved by making every district "safe" for one party or the other, as long as their numbers are proportional to the number of voters: the Proportionality Criterion has been met, and so has the Equal Voice Criterion because nobody (of either party) lives in a competitive district, but the Maximal Voice criterion has utterly failed, with the usual resulting pull towards the extremes of both parties. Indeed, the Pinks might prefer a map in which all the seats go to moderate Yellows over one in which a majority of seats go to extremist Yellows, but the efficiency gap forbids the former as too disadvantageous to the Pinks.
It looks as though these various desirable criteria for a districting system are incompatible with one another, although I haven't proven that. Another approach would be to mandate proportional representation by party, but that would reify the notion of "political party" into a system that didn't originally recognize them at all, and of which they are now only an epiphenomenon. (The U.S. Constitution, for example, makes no mention of political parties, but more-or-less-inevitably encouraged the development of a persistent two-party system, which has been in place for probably 90% of the U.S.'s existence.)
Yet another approach is to burn down the whole party system, primaries and all, and have voters vote for individuals. This isn't going to happen unless there's some kind of ranked voting system to avoid the "vote-splitting" problem (where two similar candidates split the votes of their natural supporters, and neither one gets elected).
A frequently quoted statistic: in 2016, Republicans won 49% of all the votes for House of Representatives seats in the country, but they won 57% of the seats in the House of Representatives. This is obviously wrong, but how is it wrong? Intuitively, we'd like to know that a party that gets n% of the votes should get roughly n% of the seats. (Most districting systems don't even aspire to that, but aim for "quasi-proportionality" in that the percentage of seats should be a "reasonably smooth" increasing function of the percentage of votes.)
Let's call that the Proportionality Criterion.
The recent Pennsylvania gerrymandering case was brought by Democratic voters in (I think) every district in the state, and their complaint was that their votes (and thus, in a sense, their free speech) had been devalued in advance by putting most of them into districts where their votes would make no difference: either they were "cracked" into districts that were foreordained to go Republican, or they were "packed" into 90%-Democratic districts where one more Democratic vote would make no difference. The plaintiffs claimed that most Republican voters had a much greater opportunity to affect an election. Intuitively, we'd like everybody, regardless of party or race or religion or dwelling-place, to have an equal voice in elections, in the sense that everybody has a roughly equal likelihood of affecting the outcome. To a first approximation, let's say this "likelihood" is inversely proportional to how far from 50% the vote total is in your district; if PV is the proportion of votes in a district, add up 1/(k+abs(PV-.5)) over all districts that go Yellow and see whether it's substantially different from the sum over districts that go Pink. (The "k" is a small positive constant introduced to prevent infinite results.) Call this the Equal Voice Criterion.
Of course, one can meet the Equal Voice Criterion by making every seat "safe" for one party or another, because nobody (of either party) is in a competitive district. We've seen the effect of such districting plans: candidates are more worried about party primaries than general elections, so they are dragged to the extremes of their respective parties, and we get a dysfunctional legislative body incapable of compromise. So equality of voices isn't enough: we also want to maximize total "voice", perhaps by adding up 1/(k+abs(PV-.5)) over each district regardless of who wins it. Call this the Maximal Voice Criterion.
This is maximized when PV is the same for all districts, i.e every district roughly reflects the political breakdown of the state as a whole (for a fanciful example, assign districts by the last few digits of Social Security number rather than by home address). This is probably a TERRIBLE idea: in a state with 55% Yellow voters and 45% Pink voters, it produces a 100% Yellow legislature (or Congressional delegation or whatever).
There's been a lot of talk lately about the Efficiency Gap Criterion: roughly, if the number of "wasted" votes (any vote for a losing candidate, and any vote over 50% for a winning candidate) is substantially different between parties, it suggests that somebody's cheating on behalf of one party over the other. This one is very similar to the Equal Voice Criterion, and it's equally problematic.
As pointed out in Chambers, Miller, and Sobel, the efficiency gap has a false-positive problem: in a hypothetical 100% Yellow state, there is no districting system that would produce other than a 100% Yellow legislature. Since it is impossible to gerrymander this state, any reasonable measure should find it un-gerrymandered, but the efficiency-gap measure finds a 50% efficiency gap in favor of the Pinks. (One wonders how they managed to manipulate the districting process so effectively without a single Pink in the state, much less in the legislature.) As it happens, a heavily-gerrymandered map in which the Pinks win every district by a single vote also has a 50% efficiency gap in favor of the Pinks, and the efficiency-gap criterion makes no distinction between these two opposite-extreme scenarios.
Those authors also point out that an efficiency gap of zero can often be achieved by making every district "safe" for one party or the other, as long as their numbers are proportional to the number of voters: the Proportionality Criterion has been met, and so has the Equal Voice Criterion because nobody (of either party) lives in a competitive district, but the Maximal Voice criterion has utterly failed, with the usual resulting pull towards the extremes of both parties. Indeed, the Pinks might prefer a map in which all the seats go to moderate Yellows over one in which a majority of seats go to extremist Yellows, but the efficiency gap forbids the former as too disadvantageous to the Pinks.
It looks as though these various desirable criteria for a districting system are incompatible with one another, although I haven't proven that. Another approach would be to mandate proportional representation by party, but that would reify the notion of "political party" into a system that didn't originally recognize them at all, and of which they are now only an epiphenomenon. (The U.S. Constitution, for example, makes no mention of political parties, but more-or-less-inevitably encouraged the development of a persistent two-party system, which has been in place for probably 90% of the U.S.'s existence.)
Yet another approach is to burn down the whole party system, primaries and all, and have voters vote for individuals. This isn't going to happen unless there's some kind of ranked voting system to avoid the "vote-splitting" problem (where two similar candidates split the votes of their natural supporters, and neither one gets elected).
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(an old take here: https://www.washingtonpost.com/news/wonk/wp/2014/06/03/this-computer-programmer-solved-gerrymandering-in-his-spare-time/ )
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The proposal could be seen as a non-partisan attempt to apply the Maximal Voice Criterion, in that it ensures a number of "reasonably competitive" legislative districts. However, it does a poor job on the Efficiency Gap and Equal Voice criteria too: it all-but-ensures a small number of "wasted" Democratic votes and a larger number of "wasted" Republican votes in those districts, and by encouraging a bunch of narrowly-won Democratic districts, it makes Sigma(1/(k+abs(PV-.5))) large for Democrats. And the fact that it was brought up (AFAICT) shortly after a Democratic Governor won election suggests that, like the recent nonsense in Wisconsin and Michigan (with a lame-duck Republican Governor signing bills from a continuing-Republican legislature to transfer power from the Governor to the legislature), it's an attempt to lock one party in power semi-permanently even if the people change their minds.
Wisconsin is a lovely example of a failure: Democrats won 54% of the vote statewide for state-legislative seats, but won only 36% of the legislative seats because of a previous legislature's effective gerrymandering (Proportionality failure). There must have been far more "wasted" Democratic votes than Republican votes (Efficiency Gap and Equal Voice failures); I'm not sure about Maximal Voice.
I was recently in an online discussion about shutting down polling places. There was a policy in some state that based the number of polling places in a particular neighborhood on the voter turnout rate in the previous election. I pointed out that if there's substantial partisan or racial voter suppression in one election, this policy would lock the effects of that suppression in place for several subsequent elections, even if there was no overt suppression in those subsequent elections. Which (along with the aforementioned skulduggery in New Jersey, Wisconsin, and Michigan) suggests another criterion. The Permanence Criterion tries to minimize the effect of previous elections on the outcome of this one.