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I know that in each state the voting system is first-past-the-post, a majoritarian method, but I believe that the federal aggregation, for both the president and the Congress, is approximately proportional to the population of the state.

Does this complex system approximate closer to a majoritarian or to a proportional system?

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    Could you explain your estimation as to why you believe these proportional? – hszmv Jan 23 at 20:11
  • I don't actually know how it works in detail (I am Italian who moved to Sweden) but I know that a small state gets less seats than a large state. Anyway, at least for the electoral college it looks like I am correct: en.wikipedia.org/wiki/… – Michele Dorigatti Jan 23 at 20:15
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All states are currently using a first-past-the-post system of voting for national elections and essentially majoritarian. Two states, Nebraska ans Maine, for presidential elections use per-district results for choosing electors and award 2 more to the winner of the state-wide popular vote. All other states use a winner-take-all method of assigning electors for presidential elections.

For House of representatives each member is from a district that is of approximately equal population with each state having at least one district. Each district is a first-past-the-post election. This should get a roughly proportional grouping of beliefs elected, however gerrymandering and number representatives not growing with population growth has prevented that in some scenarios.

The senate is now a statewide first-past-the-post election for each seat, as they are intentionally staggered. Selection of senator was changed in 1913 to be a popular election, previously state legislatures selected senators in any method they saw fit.

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    The Presidential election is double first-past-the-post. You have to get the most votes in a state in order to get any electoral college votes from that state, and then get the most electoral college votes. Even with two candidates a President could theoretically be elected with just over a quarter of the vote. In the unlikely event that there were more than 2 viable candidates, a President could be elected with a ridiculously low fraction of the popular vote. – DJClayworth Jan 23 at 22:00
  • Uhm - doesn't every state have at least one district? – doneal24 Jan 24 at 0:13
  • The issue that @DJClayworth is talking about has been pondered aplenty here, by the way politics.stackexchange.com/questions/13094/… – Fizz Jan 24 at 0:25
  • @DJClayworth Part of first-past-the-post is that you can win outright with a plurality. This isn't the case with the electoral college deciding who becomes president - if noone has an absolute majority, you go to a contingent election. – Andrew Grimm Feb 2 at 0:24
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You don't seem aware that senators are two per state (fixed in the constitution), regardless of the state population. That's often a lighting rod of non-proportional criticism; see e.g. the first article linked in What's (roughly) the smallest percentage of the US population that through its Senators has successfully blocked a piece of legislation?

senators representing about 11 percent of the population can filibuster a bill or those representing about 16 percent of the population can have a majority.

And there are those who argue the Senate [thus] is a bigger problem than the Electoral College from this disproprtionality perspective:

The Senate is a much bigger problem than the Electoral College [...]

America’s nonwhite population tends to be overwhelmingly in large or medium-sized states. To illustrate, the 10 biggest states (by 2018 Census estimates) all have nontrivial percentages of nonwhite voters, while the 10 smallest states mostly consist of rural, overwhelmingly white states.

While the Electoral College is also winner-take-all at the state level, each state’s representation is much more proportional to population. State are given electoral votes equal to their number of House members plus two senators. House seats are allocated to the states proportional to population. Only the extra two votes contribute to disproportionality [in the Electoral College].

Now it's true that actual majorities in the Senate have not reached anywhere near that 16%. By one calculation, the lowest was 47% (in 2017).

Note however that this is a measure of malapportionment among the two parties that by the design of the voting systems end up competing. In actual PR systems in Europe etc., the number of parties actually competing ends up [much] larger than two. It is however much more difficult to estimate these long-run effects as they would require counterfactual assumptions(*), but they are thought to be significant; see Duverger's law .

(*) For example: how many parties would emerge e.g. if the factions in the Democrat or Republican parties would split and create and their own parties instead of competing in the primaries, which are also majoritarian. Neither party is much inclined to these kinds of splits because it would be an electoral disadvantage under the present voting systems.

As an aside, since Wikipedia doesn't have great article on Duverger’s law...

Although Duverger’s central claim is that social heterogeneity will increase the number of parties only when the electoral system is sufficiently permissive, no existing study actually estimates whether social heterogeneity has a statistically significant effect when the electoral system is permissive. As a result, Duverger’s theory has never been directly tested.

The problem like I said is what is the counterfactual scenario (i.e. what are those sources of heterogeneity that would create more parties in a more "permissive" PR system). One relatively recent (but fairly cited) paper on the topic used ethnic groups as a proxy, and showed that in countries where PR is present they get a better representation.

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while the results can approximate proportional, the fact that you elect specific candidates in each district makes it majoritarian. True proportional allocates a number of seats to each party at an aggregate level, then uses some other mechanism for the members of the party to be chosen to take those seats.

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  • You are incorrect. Proportional and majoritarian are about the relationship between the voters and the elected. In a majoritarian system, the candidate with the majority of votes is elected, and the other votes are effectively lost. It is possible to have proportional and majoritarian system with both district and national voting. – Michele Dorigatti Jan 23 at 20:55
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    No, Michele, it is not. Some people incorrectly refer to ranked choice as proportional, but it isn't. You are still getting to a majority though a sort of run off system. Proportional voting systems in their true sense can only exist in councils, legislatures, etc (not single elected official posts, such as president). The number of seats each party gets is in proportion (hence the name) to votes. You can have hybrids, where half the seats are proportionate, and half are not. STV systems can be considered proportionate, but US is nothing like that. – Patrick Jan 24 at 21:16
  • I apologize. I explained myself badly. – Michele Dorigatti Feb 7 at 19:51

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