In a system of single member districts, elected for an entire legislative body all at once, is it easier to gerrymander the map to favor one party over another in a two party system, with more districts, or with fewer districts, or does it not matter?
For example, in Virginia, there are 100 seats in the state house, and 40 seats in the state senate, with all seats in both houses filled by the 2023 general election. Is it easier to gerrymander the state house, or the state senate, or is there no difference, if one party is in full control of the process?
- A legislative body is "easier to gerrymander" if it is possible to cause more seats in the legislative map for the body to favor the party drawing the map, taking the geographical distribution of political preferences and turnout likelihood in the territory served by the legislative body constant.
Assume that the districts must be contiguous and have effectively equal populations, but that there are no other regulations for map drawing which is done by a single political party that controls all levers of power.
Assume that a legislative body can have no less than five and no more than 650 members.
Assume that the population of the overall territory served by the legislative body is at least 6.5 million.
Assume that politically preferences are inhomogeneous to an extent within the range of inhomogeneity found in larger U.S. states.
Assume that expected turnout is not necessarily uniform from one district to another with variation in turnout rates within the range found in larger U.S. states and is fairly strongly correlated with political preferences.
Assume that there are only two political parties, that each district has one candidate from each party, and that there are no independent or write-in candidates. These assumptions, among other things, eliminate any differences between systems that require a plurality to win, systems that require a majority to win, and instant runoff voting, for example.
This answer should have a mathematically determinable answer, or set of answers that involves varying factors like turnout and inhomogeneity of political opinion with geography.
But, I've never seen the answer to this question clearly stated, and I don't have a good intuition one way or the other.
In a completely homogeneous distribution of political preferences, all maps have the same outcome (100% of the seats will favor the party with a larger share of the total).
In general, single member districts tend to produce legislative majorities that are greater than the percentage of voters that favor the party that gets the most legislative seats. Single member districts tend to amplify differences in popular vote support relative to proportional representation. The most common example of this in the real world is the electoral college.
I'm aware that this question glosses over (perhaps inappropriately) the choices that a map maker in full control has between making their districts safer in the event of a shift in political opinion after the map is drawn, and winning more districts that may be more competitive.