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The US is famous for being heavily influenced by gerrymandering, to the point where some of the districts look absolutely ridiculous to the plain eye. The obvious solution is to use some sort of a deterministic mathematical formula for dividing a territory into equal parts, so that no side gets an advantage.

But have any countries actually implemented such a policy? I know gerrymandering is easy to avoid altogether by using proportional voting, however I'm curious about systems that do have voting districts.

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    This doesn't avoid gerrymandering. It shifts it to the selection of the deterministic mathematical formula. Because some side will always get some advantage under some circumstance. So the question will be who can better manipulate creation of the formula to match their needs. – Brythan Jun 30 '17 at 1:40
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    "being heavily influenced by gerrymandering" FiveThirtyEight called, they said your sources are way wrong. "Gerrymandering and other partisan efforts at redistricting do play a role, but it is mostly around the margin. A study by John Sides and Eric McGhee found that redistricting after the 2010 Census, which was controlled by Republicans in many key states, produced a net swing of only about seven House seats toward Republicans.. Fake news is so fake. – user4012 Jun 30 '17 at 3:32
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    @Brythan, Re "some side will always get some advantage under some circumstance": that always doesn't match those somes -- it amounts to "some side sometimes gets some advantage". The goal of such algorithms being to minimize such occasional advantages impartially -- Governor Gerry's goal was the opposite -- maximizing his party's advantage. Unless someone has a proof that all such algorithmic maximums and minimums are necessarily equal or virtually equal, then better districting algorithms remain a worthy goal. – agc Jun 30 '17 at 4:00
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    @user4012 - two points to that - 1) swinging seven seats is a pretty huge deal. 2) your "seven seats" hand-waving seems to assume that there was never any gerrymandering in place before, vs having been done, increasingly, over many, many years. That seven seats represents an increase in the effect of gerrymandering, not the total amount. – PoloHoleSet Jun 30 '17 at 14:44
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    @user4012 One effect of bi-partisan redistricting is gerrymandering to create safe seats. That way both sides know that they don't have to spend resources fighting for those seats at election time, and can then hand the candidacy to those seats to whatever party hack they owe a favour to. This doesn't show up as a party imbalance in the number of seats won, but rather a lack of real competition within each seat. – Paul Johnson May 22 '18 at 12:51
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While this does not truly address OP's question about other countries, there are states in the USA which, while not purely from mathematical formula, use objective, consistent criteria for drawing their lines.

They way they do this is, by law, instead of the "winning" party getting to drive the process, the process is always done by a non-political, non-partisan body (very, very different from "bi-partisan").

Iowa is the most well-known example of this -

Boston Globe: Iowa redistricting takes the partisanship out of mapmaking

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    And the Iowa non-partisan commission drew three Republican districts and one Democratic district. Meanwhile, it would have been trivial to have drawn two Democratic districts and two Republican districts, matching the partisan lean of the state. In California, Democrats should outnumber Republicans, but there are more Republican voters than are seen in the congressional results. Allegedly "non-partisan" commissions are heavily vulnerable to partisan manipulation or simple luck. And, as you note, this doesn't answer the question. – Brythan Jun 30 '17 at 15:24
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    @Brythan - the question is asking for a foreign non-biased example, based on the assumption that all the USA methods are biased, so it is addressing what they wanted, it just doesn't accept the flawed assumption. Your assumption is also flawed. A "district" is a local sub-division of the state. It is very much geographically based. This idea that the number of districts has to match the total partisan breakdown of the state is an artificial one. Iowa having a three to one breakdown does not represent a flaw. Also, the fact that three voted that way this time does not make it always so. – PoloHoleSet Jun 30 '17 at 15:32
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    If we took a poll of how voters self-identify and tried to artificially create a result that would always match that, that would be a form of gerrymandering, itself. There would be no point to having candidates or elections, no point in having politicians discuss issues if you are going to artificially impose a partisan-centered result like that. Artificial "equality" is just as artificial as an skewed partisan result. – PoloHoleSet Jun 30 '17 at 15:34
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    @Brythan Actually, it wouldn't have been "trivial" to create 2 Democratic districts. If, in an attempt to get 2 Democratic districts, you took 28,000 Democratic votes from the only Democratic district and transplanted them into the district the Republicans won most narrowly, the result would instead have been 4 Republican districts, at least for this election. But this was an election where Trump won Iowa by over 9 points. In 2018, one of those Republican districts could easily swing Democratic, if the winds blow the other way. – D M Jun 30 '17 at 15:58
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    "Non-partisan" is not the same as "objective". By definition, "objective" criteria would be criteria that produce the same answer every time, no matter who is doing the deciding. – William Jockusch Apr 17 at 13:35
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This is a difficult question to answer because any answer will be heavily dependent on one's definition of bias. To attempt to answer, I'll be working off of the Merriam-Webster definition of gerrymandering:

to divide (a territorial unit) into election districts to give one political party an electoral majority in a large number of districts while concentrating the voting strength of the opposition in as few districts as possible

I believe that Norwegian system of reapportionment avoids both prongs of this definition of gerrymandering. Wikipedia outlines the Norwegian process:

Out of the 169 seats in the Storting, 150 are apportioned among the 19 Counties of Norway with deliberate bias in favor of rural areas. The number of seats for a county is decided using a formula in which a county receives 1 point for every inhabitant and 1.8 points for every square kilometer of land area. However, the bias is reduced by the 19 compensation seats, which are given to parties that are underrepresented. Thus the system does not have a great effect on the partisan composition of the Storting, but does result in more MPs coming from rural counties. Electoral researcher Bernt Aardal calculated that if the 2009 parliamentary election had been conducted without this bias, the Labour Party and Progress Party would both have lost a seat, while the Red Party and Liberal Party would each have gained one, reducing the majority of the Red-Green Coalition from 3 seats to 1.

Specifically:

  1. Does the Norwegian system divide election districts to give one political party an electoral majority?

    • According to a well-credentialed political scientist, removing geographic weights in the system would have been inconsequential in its outcome. Check out his research (which highlight several other, perhaps even more proportionately designed, electoral systems) (Aardal, B. (2011). The Norwegian Electoral System and its Political Consequences. World Political Science, 7(1), pp. -. Retrieved 30 Jun. 2017)
    • The proportionate design of the Norwegian system gives less prominent party organizations more power than the US system does.
    • The geographic districts remain largely the same over time
  2. Does the Norwegian system concentrate the voting strength of the opposition (in this case, we'll assume that's the minority party(s)) in as few districts as possible?

    • Since the geographic weights are counterbalanced with compensation seats, no geography would be disproportionately favored (as outlined in the Aardal study).
    • The majority party cannot punish the minority party by changing or modifying district geographies once in power

In conclusion, I believe that the Norwegian system avoids both 1 and 2, uses a mathematical formula, and therefore satisfies the requirements of this question.

I'm also sure that several other countries have similar systems and I'm sure the study I've linked provides further insight into how they work/operate.

  • This isn't responsive to this question. This question: does any country use a mathematical formula for dividing into equal parts. This answer: Norway doesn't try to divide into equal parts and instead uses two formulas to compensate for that unequal division. The very existence of compensation seats reinforces my point that there is no way to fairly determine geographic districts. – Brythan Jun 30 '17 at 14:55
  • The question literally reads " divide districts, so that gerrymandering is avoided". This answer is responsive to that question OP mentions an "obvious solution" being equal parts but doesn't ask about countries that use equal apportionment. – LearnWorkLearn Jun 30 '17 at 15:09
  • The title is a summary, not the question. The question says "dividing a territory into equal parts" and "But have any countries actually implemented such a policy?" – Brythan Jun 30 '17 at 15:19
  • "The obvious solution is to use some sort of a deterministic mathematical formula for dividing a territory into equal parts, so that no side gets an advantage." "But have any countries actually implemented such a policy? I know gerrymandering is easy to avoid altogether by using proportional voting, however I'm curious about systems that do have voting districts." Agree to disagree @Brythan -- just because OP suggests an answer to his own question doesn't mean it's the only answer. – LearnWorkLearn Jun 30 '17 at 15:31
  • (-1) Norway uses PR, gerrymandering is a lot less relevant. The OP might have been a bit imprecise in his choice of words but the intent behind the question seems clear to me and this answer does not address it. – Relaxed Jul 1 '17 at 9:24
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In South Australia there is a "Fairness Rule", which in practice requires the boundaries to be redrawn after each election so that the party which won the two party preferred vote would have won the election. This does tend to favour the major parties somewhat, but does prevent excessive gerrymandering.

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I don't know if such a policy has ever been used. But it's worth noting that such policies do exist. For example, one could implement a law that says that anyone can submit a proposed set of districts after a census, and the proposed set of districts with the lowest average distance between a pair of voters in the same district wins.

For another possibility, one could define the "diameter" of a district to be the greatest crow-flies distance between any two points in the district, and say that the winning set of districts is the one in which the average diameter of all the districts is lowest.

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