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A common theme in electoral reform is adjusting the way representatives are selected using the results of an election: multi-member districts, ranked-choice-voting, party-proportional representation, etc.

I'm curious if there are any bodies that use another approach -- assigning differing amounts of "voting weight" to different representatives.

That weight might be based on the size of the representative's constituency, the proportion of votes that they received in their election, or some other factor like the historical significance of the district.


For example, consider a hypothetical country that has 6 states, Micria, Tinia, Smallia, Media, Largia, and Hugia, with very different populations:

State Population Proportional Weight
Micria 1k 0.1
Tinia 10k 1
Smallia 20k 2
Media 30k 3
Largia 40k 4
Hugia 50k 5
Total 151k 15.1

The typical "solution" to give a "fair" representation of the people in each state is to elect a different number of representatives from each state; since Hugia has 5x the population of Tinia, it would have (roughly) 5x the number of representatives.

However, for this country, this is difficult, because Hugia has 50x the population of Micria, and so they would need to have a very large number of representatives (151) for their relatively small country of only 151k people.

Instead, they opt to elect only a single representative from each state. However, when the legislature makes votes, it is not a simple majority of representatives which is necessary, but a majority of the "proportional weight":

Representatives Simple majority Proportional majority
Micria + Tinia + Media + Hugia Yes (4/6) Yes (9.1 / 15.1)
Micria + Tinia + Smallia + Media Yes (4/6) No (6.1 / 15.1)
Media + Hugia No (2/6) Yes (8 / 15.1)

This system has some clear advantages and disadvantages.

A small number of representatives can achieve a very fair representation; this can simplify legislative processes and reduce the overhead of larger bureaucracies.

It also makes it much easier to make apportioning adjustments without messy processes like redistricting, which may separate constituents from long-time representatives or introduce their own political biases.

On the other hand, this gives apparently equal platforms to extremely unequal legislative influences; for example, the Tinia representative has one fifth the power of the Hugia representative, but could appear equal in debates, press-conferences, etc. In addition, depending on how the representatives are elected, this may exacerbate inequities in representation; for example, first-past-the-post elections could effectively disenfranchise 49% of the population of Hugia, while giving a not particularly liked representative a power almost like a mandate in the legislature.


Are there any real-world examples of such legislative bodies, where two different members of the same body have different "weights" behind their votes?


Here are some related voting processes I'm aware of, but aren't what I'm looking for:

  • Districts with vast differences in constituency size, power, etc, but equal representation
    • For example, the US senate, where each state gets 2 representatives, despite wildly different demographics in each state. However, each senator receives a single vote, and processes move forward by a (super)majority of representatives
  • Non-voting members in legislature
    • This is an extreme form of this process, where some legislatures have members which can officially be involved in the legislative process, but are unable to cast votes. For example, the US has non-voting representative members of the House to represent non-state territories like Puerto Rico, D.C., and American Samoa.
  • Minority rule provisions which require assent by a certain minority of representatives to pass certain measures
    • For example, Bosnia and Herzegovina have a legislature of 3 groups. A quorum requires not just a supermajority of the overall body, but also a majority of each of the groups. I don't consider this to be what I'm looking for, because the members don't have equal titles (they are explicitly assigned to each of the minority groups whose interest they represent), and because votes aren't enacted by a simple majority of weight
  • Proportional representation approaches like party-proportional voting
    • Some legislatures assign additional seats to parties winning more votes to ensure that the resulting composition of the legislature matches the composition of the votes. For example, the German Bundestag adds additional seats to approach proportionality. However, each representative still has only a single vote after this adjustment is complete.
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    Anyone thinking about weighted voting needs to understand that voting power doesn't equal the weight of the votes. see en.wikipedia.org/wiki/Banzhaf_power_index for example. In your nation, Micria has no power at all! There are no situations in which they could swing a vote (but if hugia only had 4 votes, then Micria could have a lot of power!)
    – James K
    Jan 15 at 6:46
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    @JamesK: Yes that was my first thought too! Worth noting, though, that Micria can have some influence in practice, eg if (in a particular vote) Tinia either abstains, or is for some reason barred from voting.
    – psmears
    Jan 15 at 13:37
  • The president of India is chosen by an electoral college consisting of four classes of legislators, whose votes are variously weighted, both within and across classes. Jan 15 at 23:09
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    There are some glaring issues here. You're assuming that a state votes unanimously. In your representative-based system, Micria cannot represent a divided populace (one vote = one voice), and Hugia is unlikely to ever vote in a unanimous way. In your weighting-based system, you've created the Micria problem for all states, now not even the most populous state can have a vote that is not unanimous. For a question that tries to be very precise about its proposed fairness (e.g. not allowing rounding/approximation in the representative-based system), I think this is a HUGE flaw.
    – Flater
    Jan 18 at 3:15

7 Answers 7

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Are there any real-world examples of such legislative bodies, where two different members of the same body have different "weights" behind their votes?

Yes. The Council of the European Union is not a directly elected legislature (its members are Cabinet ministers of EU member states), but it is one of the two legislative bodies of the EU and its members are ultimately determined through national democratic elections in each member country. And on many issues, the Council operates through qualified majority voting. A measure can’t pass unless it has 55% of members voting “yes,” and those members have to represent 65% of the EU’s population. The German representative and the Luxembourg representative contribute equally to the 55% requirement, but the German representative has a much larger vote when considering the 65% requirement.

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    Ah of course, I misunderstood the structure at first. That's a great example; representatives have the "weight" of their population, but there's also a "minority rule" protection that a simple super majority is necessary. Jan 15 at 8:55
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    There exists a mathematical analysis in terms of power indices for the Council: The work by Olga Birkmeier I cite in my answer covers both the EU council and the German Federal Council.
    – ccprog
    Jan 15 at 15:56
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A minor, but important example was the Nassau county board. It had six members with weighted votes.

Hempstead #1: 9
Hempstead #2: 9
North Hempstead: 7
Oyster Bay: 3
Glen Cove: 1
Long Beach: 1

But this issue with this is that, once the Hempsted votes had been counted, the votes of the other three representatives could never swing the vote. Oyster bay, Glen cove and Long Beach had 16% of the votes, but 0% of the power.

Analysise of this resulted in the rediscovery of the Banzhaf power index

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Federal Council (Bundesrat) of Germany

The Federal Council is the second chamber of the German Parliament. It represents the governments of the sixteen member states. Each government has a different number of seats, but is only allowed to cast its vote as a single bloc.

So formally, when the council president calls a vote, he/she asks for the votes of each state. When he/she asks for, lets say Thuringia, only the Minister President answers with "yes", and four votes in favor are registered. This is effectively the same as if he was casting one vote with a weight of four.

The number of seats vary between three and six per state. That does not equalize the difference in their size, but only dampens the effect. While the number of inhabitants of Bremen and North Rhine-Westfalia differ by a proportion of 1 / 26, the number of their votes differ 1 / 2.

Article 51 of the Basic Law for the Federal Republic of Germany describes the rules:

(1) The Bundesrat shall consist of members of the Land governments, which appoint and recall them. Other members of those governments may serve as alternates.

(2) Each Land shall have at least three votes; Länder with more than two million inhabitants shall have four, Länder with more than six million inhabitants five and Länder with more than seven million inhabitants six votes.

(3) Each Land may appoint as many members as it has votes. The votes of each Land may be cast only as a unit and only by Members present or their alternates.

The resulting membership looks like this:

State Inhabitants Votes Inhabitants per Vote
Baden-Württemberg 11,023,425 6 1,837,238
Bayern 12,997,204 6 2,166,201
Berlin 3,613,495 4 903,374
Brandenburg 2,504,040 4 626,010
Bremen 681,032 3 227,010
Hamburg 1,830,584 3 610,195
Hessen 6,243,262 5 1,248,652
Mecklenburg-Vorpommern 1,611,119 3 537,040
Niedersachsen 7,962,775 6 1,327,129
Nordrhein-Westfalen 17,912,134 6 2,985,356
Rheinland-Pfalz 4,073,679 4 1,018,420
Saarland 994,187 3 331,396
Sachsen 4,081,308 4 1,020,327
Sachsen-Anhalt 2,223,081 4 555,770
Schleswig-Holstein 2,889,821 4 722,455
Thüringen 2,151,205 4 537,801
Total 82,792,351 69 1,199,889

A regularily noted consequence of this distribution is that the four states with six votes represent more than half of the inhabitants of Germany, but have no majority in the council. They only have what is called a Sperrminorität, which means the other states cannot achieve a super majority (two thirds of the votes, needed for changes to the Basic Law) against them.

A mathematical analysis of this distribution in terms of power indices – both Penrose/Banzhaf and Shapley/Shubik – was published in

Olga Birkmeier: Machtindizes und Fairness-Kriterien in gewichteten Abstimmungssystemen mit Enthaltungen. Deutschland, Logos-Verlag, 2011.

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  • It would be interesting to know how politically sustainable it is to still keep more than one member per state while you could make do with only one person and use a figurative weight to achieve the same result, possibly saving in any cost associated with the other people (I am assuming they are given a salary and reimbursement for costs incurred in being part of the body)
    – bracco23
    Jan 15 at 17:14
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    @bracco23 All members of the council are members of state governments, and the only specific renumeration they get is travel costs in the form of a unlimited Deutsche Bahn railway network ticket.
    – ccprog
    Jan 15 at 17:31
  • @bracco23 Also, while the votes are normally anounced by the Minister President, it is common that during deliberations, specific ministers will speak about issues pertaining to their ressort.
    – ccprog
    Jan 15 at 17:36
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In the Electoral colleges for the senate in The Netherlands, different members' votes are weighted differently. It is an elected body, but not a legislative body. The sole role of this electoral college is to, together with members of the provincial parliaments, elect the senate, such as in the 2023 Senate Election:

The weight of each elector's vote is determined by the population of the province or special municipality which the elector represents, at a ratio of approximately 1 vote per 100 residents.

The electoral weight for the electoral college of non-residents is covered by this answer.

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#Germany

Not a parliament, but an elected body: The workers' council in German employee law, who represent the workers and can make agreements with the company leadership. Similar to a union, but on a more local level.

At the level of an individual site, each member has one vote. However, when a company has multiple sites, a council representing all of those sites together is established, and in this one the members have votes equal to the number of employees in each site(*), so that while they all share the same role, position and "title" if you will, their votes can have vastly different weights.

(*) actually, if want to nitpick, since each site sends two representatives to the general council, each of those two has a vote equal to half of the number of employees on their site.

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This may not be what you're looking for, but in 48 US states, the presidential candidate who gets the most votes gets ALL of the states electoral votes, which is approximately proportional to population.  But if no candidate gets a majority, the house of representatives has to choose, and in that case, each state gets one vote.

So, for example, in 2020, 42% of California voters voted for Biden, but the result was the same as if it had been 100%.  (There is currently a lawsuit claiming that violates the Constitution.)  But if Biden had not got a majority of electors, California would get one vote in the house. So the election is somewhat proportional, but the fallback (by state) is not.

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In corporations, someone who has gathered more proxy votes has more voting power than someone with fewer.

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    The question asked about elected bodies, the restatement of the question further down the text about legislative bodies. Your answer pertains to none of them.
    – ccprog
    Jan 15 at 19:06

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