How Feasible Is Creating a Gerrymander-Free District-Mapping Program?

[lpetrich]

For the actual voting part, there are alternatives to first-past-the-post or plurality voting, alternatives that are much more multicandidate-friendly. A simple one is runoff elections. The top two of the first election then go head-to-head in a second election. Another one is preference voting. One ranks the candidates by one's preferences, and these ballots are then counted up to give the overall winner. There are a variety of algorithms for doing so, and a commonly-used one is Instant Runoff Voting, a sequential-runoff algorithm. In each round of counting, for all the candidates remaining in the race, the top preferences are counted up, and whoever gets a majority wins. But if no candidate gets a majority, then the candidate with the fewest votes gets dropped from the count. DemoChoice Polls has polls that use IRV, and you can see how the counting works in them.

 

[lpetrich]

But why stick with single-member districts? Why not multimember ones?

One can extend IRV to multimember districts with the Single Transferable Vote. In each round, a candidate wins if that candidate gets more than some victory threshold. The candidate's "excess" votes continue in the count, with the victory-threshold number of them being dropped from the count. Alternately, all the candidate's votes could get reweighted by multiplying their weights (initially 1) by (number of excess votes) / (number of total votes).

But a more common system is proportional representation. In its purest form, each party gets a number of seats in proportion to how many votes that it got. Parties usually publish lists of candidates that they want to seat, so this is called the party-list system. There are mixed systems, with both district seats, each member being elected by some district, and list seats, with members selected in party-list fashion. The list-seat members may be selected to make the whole body proportional (mixed-member), or else only those seats proportional (parallel).

I myself have written some vote-counting code, to see what different algorithms produce.

 

[anorlunda]

My state, Vermont, has a much simpler solution. We have fewer than 711,000 people, so the whole state is one district.

I must plead guilty to this, in all honesty. My proposal would likely lead to functionally increasing the voting strength of the minority, but the degree to which this would occur could be mitigated by limiting the "area of overlap" of the computer generated congressional districts solely created by normalizing population and geography within a state. But I confess, prioritization of demographic diversity is a reflection of my belief that it would be beneficial to the country as a whole.

I don't think you realize that demographic diversity works to weaken the strength of the minority. Let's say the population was 60% ying and 40% yang. Perfect demographic diversity with a winner-take-all system produces a result where ying gets 100% of the seats. That is why the US Voting Rights Act, specifically prohibits demographically diverse districting, but instead mandates some districts where the minorities can win.

But a more common system is proportional representation. In its purest form, each party gets a number of seats in proportion to how many votes that it got.

This is a better solution than playing with districts. If we ever have a constitutional convention where we have the opportunity to change everything, that is one of the things to consider.

Even without the districting question, even without elections, the proportional representation principle can be used. For example, the Tea Party minority elected in 2010-2012 might have had more influence if they remained a third party, rather than becoming a minority wing of Republicans (ditto for the black Caucus wing in the Democrats). With a 2 party system, when a compromise is negotiated, the Democratic majority deals with the Republican majority. But in an N party negotiation (N>2), the compromise generally gives each party at the table at least some of what they want. So the key strategy for minorities is to gain a seat at the table.

 

[jack action]

I never understood the need to officially incorporate parties in the election process. IMHO, this goes against the democracy concept (one person, one vote; 50% + 1 majority). It seems that everybody wants to alter - and complicate - the actual party system such that it represents more the 50% + 1 majority. Why not just do the democratic thing and vote directly for the head office candidate. Why do we vote for someone who will vote for the head office candidate? If my "surrogate" of choice doesn't get elected, then my vote doesn't count, which is anything but democracy. Worst, my "surrogate" can decide to change his/her mind and vote differently, decide to change party or become independent (basically removing all of his/her power).

I have looked for an answer as to why parties were introduced into democracy and what were they supposed to accomplished, but never found one. For example, in cities (at least here in Canada), you can have parties or not, but we still elect the mayor AND the local counselor.

I don't mind that parties do exist such that a candidate can clearly show what he/she stands for, but I don't understand why these parties are incorporated into the election system. An independent representative shouldn't have less power than one that is part of a party, like for spending or time available to speak in chamber.

 

[anorlunda]

@jack action , you are questioning the premise of the Republic form of government. Parties add a second level of representation.

That's fine, but you won't find explanations of you don't use the right search term.
https://en.m.wikipedia.org/wiki/Republic

 

[Mark44]

IMHO, this goes against the democracy concept

The U.S. isn't a democracy. The Founders designed a constitution for a country that would explicitly not be a democracy. @anorlunda has it right...

@jack action , you are questioning the premise of the Republic form of government. Parties add a second level of representation.

 

[jack action]

@anorlunda , from your reference:

Elections

In liberal democracies presidents are elected, either directly by the people or indirectly by a parliament or council. Typically in presidential and semi-presidential systems the president is directly elected by the people, or is indirectly elected as done in the United States. In that country the president is officially elected by an electoral college, chosen by the States, all of which do so by direct election of the electors. The indirect election of the president through the electoral college conforms to the concept of republic as one with a system of indirect election. In the opinion of some, direct election confers legitimacy upon the president and gives the office much of its political power. However, this concept of legitimacy differs from that expressed in the United States Constitution which established the legitimacy of the United States president as resulting from the signing of the Constitution by nine states. The idea that direct election is required for legitimacy also contradicts the spirit of the Great Compromise, whose actual result was manifest in the clause that provides voters in smaller states with slightly more representation in presidential selection than those in large states.

In states with a parliamentary system the president is usually elected by the parliament. This indirect election subordinates the president to the parliament, and also gives the president limited legitimacy and turns most presidential powers into reserve powers that can only be exercised under rare circumstance. There are exceptions where elected presidents have only ceremonial powers, such as in Ireland.

The keywords are "indirectly elected", which is what I consider against the principles of democracy. I'm not here to judge the legitimacy of one process over another. But what I think the OP wants to achieve and when the subject of proportional representation was raised, these seem complications of the system in place (indirect election) to mimic a democracy (direct election or one person, one vote). My point is, instead of trying to create all of these complicated modifications (which will surely introduce a whole new set of loop holes) to mimic accurate people representation, why not simply do the direct election instead?

Which I simply put in an earlier post:

I think the problem is this system where you vote for someone who will vote for you.

 

[anorlunda]

My point is, instead of trying to create all of these complicated modifications

I don't dispute that point. I was trying to help you with the following point.

I have looked for an answer as to why parties were introduced into democracy and what were they supposed to accomplished, but never found one.

 

[jack action]

I don't dispute that point. I was trying to help you with the following point.

It doesn't talk about parties in your reference. But it did force me to look for more. So, what I'm referring to is called a non-partisan system. I found the origin of political parties, but that doesn't explain why having political parties deeply incorporated in the elective process is considered an advantage for the people (seems to be one only for the people in power).

Fun fact, I learned that George Washington was against political parties:

Washington continues to advance his idea of the dangers of sectionalism and expands his warning to include the dangers of political parties to the country as a whole. These warnings are given in the context of the recent rise of two opposing parties within the government—the Democratic-Republican Party led by Jefferson, and Hamilton's Federalist Party. Washington had striven to remain neutral during a conflict between Britain and France brought about by the French Revolution, while the Democratic-Republicans had made efforts to align with France and the Federalist had made efforts to ally with Great Britain.

Washington recognizes that it is natural for people to organize and operate within groups such as political parties, but he also argues that every government has recognized political parties as an enemy and has sought to repress them because of their tendency to seek more power than other groups and to take revenge on political opponents. He feels that disagreements between political parties weakened the government.

Moreover, he makes the case that "the alternate domination" of one party over another and coinciding efforts to exact revenge upon their opponents have led to horrible atrocities, and "is itself a frightful despotism. But this leads at length to a more formal and permanent despotism." From Washington's perspective and judgment, political parties eventually and "gradually incline the minds of men to seek security... in the absolute power of an individual", leading to despotism. He acknowledges the fact that parties are sometimes beneficial in promoting liberty in monarchies, but argues that political parties must be restrained in a popularly elected government because of their tendency to distract the government from their duties, create unfounded jealousies among groups and regions, raise false alarms among the people, promote riots and insurrection, and provide foreign nations and interests access to the government where they can impose their will upon the country.

Written 220 years ago and I feel like I'm reading the description of the political atmosphere of today.

 

[SlowThinker]

I have looked for an answer as to why parties were introduced into democracy and what were they supposed to accomplished, but never found one.

(Should not this thread be moved somewhere else?)
One idea is, I don't really have the time to run my country, so I'd rather give my voting power to someone who does have the time to watch the news, plan the roads, etc. This naturally leads to an indirect democracy. Then the electees (sorry English is not my first language) naturally form groups of similar world views.
Obviously giving someone power and not checking how they use it, is a bad idea.
But in a direct democracy, media can shape the popular vote with ease. So which is better? Who checks the media?

 

[lpetrich]

(Should not this thread be moved somewhere else?)

Or at least the posts on whether we ought to have political parties -- and separated from discussion of anti-gerrymandering algorithms and vote-counting algorithms in general.

There are some interesting algorithms for counting preference votes that involve a "Condorcet matrix", a matrix of how many ballots where each candidate beats each other candidate. Thus turning the votes into a virtual round robin contest. If some candidate beats all the other candidates in this way, then that candidate is a "Condorcet winner". But there may be no Condorcet winners, and there are a variety of algorithms for finding a winner in such a case.

 

[jack action]

There are some interesting algorithms for counting preference votes that involve a "Condorcet matrix", a matrix of how many ballots where each candidate beats each other candidate. Thus turning the votes into a virtual round robin contest. If some candidate beats all the other candidates in this way, then that candidate is a "Condorcet winner". But there may be no Condorcet winners, and there are a variety of algorithms for finding a winner in such a case.

But what is the advantage of using such an algorithm over the old 50% + 1 majority?

We have to remember what is the aim here. It is not to determine some winner in a made-up game. It is people giving some of their powers to someone else. If someone wants to give it to A and have no trust at all in B, that should be respected. We shouldn't assume B is an acceptable replacement for that person or force that person to say B could be a good second choice.

When you start using all of these complicated algorithms, you always introduce some loop holes to determine the winner. And the funny thing is that the main objective of these algorithms is to better represent the 50% + 1 majority. So why not use it appropriately instead?

I remember a race for a party leadership a few years ago. They were 4 candidates; Two were favorites and head to head, the two others were clearly not favorites (both with less than 18% each on the first ballot). The 4th runner quit after the 2nd ballot and gave his support to the 3rd. On the third ballot, one the favorite became third at the surprise of everyone and had to quit (because of the rules in place). On the fourth ballot, the supporter of that favorite who had lost were so pissed and hated so much the remaining favorite candidate that they decided to vote for the "other guy" and he won. At the next election, the party was so weak - and it was clearly due to its lack of leadership - that it scored their lowest percentage in the party's history to that date.

This is the perfect example of how a guy with an 18% approval gets elected in an unforeseen way and, in the end, everybody is a loser. To me, there is no replacement for the 50% + 1 majority and if you don't get it, you repeat the process until you do. There is no other way. That is what they do when they elect a pope (two-third supermajority) or when a jury makes a decision (unanimous verdict), so why be different when you elect someone with a simple 50% + 1 majority?

 

[SlowThinker]

To me, there is no replacement for the 50% + 1 majority and if you don't get it, you repeat the process until you do. There is no other way. That is what they do when they elect a pope (two-third supermajority) or when a jury makes a decision (unanimous verdict), so why be different when you elect someone with a simple 50% + 1 majority?

Well , I'll ask the obvious: who would be running the country for the next 20+ years, that is, before such a majority is reached?

Also, who says that making 50% happy is better than making 70% somewhat happy?

 

[jack action]

The running of the country is not in danger if majority is not reached. I'm OK with the "top" candidate being in office, but if he/she doesn't have 50%+1 of the electorate (not just the ones who voted), then his/her only priority would be to hold another election (say within a year).

Of course, with today's politic, it may seems inconceivable (where we see 50% as a goal instead of a bare minimum; 100% should be our idealistic goal), but IMO it wouldn't be long that politicians would change their strategies to gain full power and waste less time in elections. People would get tired of elections too and demand more from their candidates. One thing that would surely change is that they would all encourage people to vote (if only 40% of people vote, you can't go over 50%, can you?), which is not the case right now, as only people who vote for them are encouraged, just enough to get 50% of voters only. Lots of algorithms are used to that end.

 

[lpetrich]

But what is the advantage of using such an algorithm over the old 50% + 1 majority?

Because with more than two candidates, one will not necessarily get such a majority. What should one do then?

 

[lpetrich]

I'll go through the Condorcet algorithms that I've implemented.

Schulze's beatpath method. Tries to find every beatpath that goes through all the candidates and then uses the strongest one. A beatpath goes the route of pairwise victories: C(cand,next) > C(next,cand) for each candidate in it for their Condorcet matrix C. Its strength is its smallest C(cand,next) value. This is equivalent to the widest-path problem in graph theory, and it can be solved with a variant of the Floyd–Warshall algorithm.

Copeland's method. The winner has the largest value of (pairwise victories) - (pairwise defeats).

Minimax methods. The winner has the smallest value of (largest value of score(other,cand)), the one that the other candidates did the worst against. Score methods for candidates A and B:
Winning votes: if C(A,B) > C(B,A) then C(A,B) else 0
Margins: C(A,B) - C(B,A)
Pairwise Opposition: C(A,B)

Kemeny-Young method. Find the permutation of candidates which maximizes the sum of C(earlier,later) for all (earlier,later) pairs in the permutation.

Dodgson's method. Go through all the permutations of ballot orderings, applying each permutation to all the ballots and finding the Condorcet winner, if any, for the permuted ballots. The overall winner is the Condorcet winner with the smallest "permutation distance" from the identity permutation. That distance is the smallest number of 2-permutations needed to create the permutation, and it equals (length) - (number of cycles). A candidate that was never a Condorcet winner gets permutation distance (length).

Tideman's ranked-pairs method. It is a simple hill-climbing version of the Kemeny-Young method. One selects an ordered pair with the largest C(first,second) value. then continues with the other C values in order if doing so creates no cycles. Once that is done, one sorts the candidates using those pairs' ordering, and whichever one comes out on top is the winner. Here is a cyclicity tester: find which candidates are always winners and which ones are always losers. Remove all pairs containing them and repeat this algorithm until one can go no further. If no pairs are left, then there are no cycles, and the graph of pairs is a Directed Acyclic Graph.

Maximal lotteries generalizes the Condorcet winner to a probability vector p. Find it in this fashion. Find the difference D = C - transpose(C), and then find p such that p.D > 0. This can be done by linear programming: maximize w with p.D >= w, with the constraints that all the p's are >= 0 and their sum = 1.

 

[Vanadium 50]

Because with more than two candidates

And now we're getting into Arrow's Theorem, which states (in layman's terms) that there is no perfect voting systems.

Many of the messages in this thread are not really against gerrymandering. They are more about using different gerrymandering schemes for positive social outcomes. (And, indeed, the US Voting Rights Act of 1965 mandates some gerrymandering)

 

[jack action]

Because with more than two candidates, one will not necessarily get such a majority. What should one do then?

Then you do not accept the results and repeat the process with different variables.

You are still asking to choose an algorithm between an infinite amount of possibilities that will all give different results. Again, politicians in power will make sure the system in place favors them.

You have to remember that the objective is not to find a winner. The objective is to find someone who represents the electorate. Assuming they are 20 candidates and the "winner" has only 10% of the vote, is this acceptable? Can a candidate having only 1 out of 10 people voting for him/her can claim representing the entire group? At this point there are only two solutions possible, both implying a new election:

1. Candidates mus change their promises about the dividing issue;
2. Candidates must promise not to take care of the dividing issue (maybe leaving it to a more local government).

The only satisfactory result is unanimity. For very large groups, this is almost impossible and 50% + 1 is the only number that makes sense to define a majority clearly (otherwise, with supermajority, why 2/3? why 75%?). Although I can accept such a low number in a tight race, I think it is really stupid to set it as a goal or even celebrate victory when someone sadly wins with such a low number. If such a low number is expected, forget wasting money on an election an go back to my previous points 1 & 2.

 

[RogueOne]

Do you think gerrymander-free districts would have changed the 2016 election? Of the (approximate) 3100 counties in the U.S, 2600 of them voted republican. 500 counties voted democrat. Their desires might better be met by their local governments, since the democrat majorities are highly concentrated into 16% of the geographical united states.

Ideas like that are why this is not as objective or black-and-white as we would like to think. There are many ways to interpret this reality. To make a decision that can be considered objective, there would need to be a universally understood reality of the same set of facts.

Would you have voters vote on whether or not the district-mapping program was acceptable?