I admit that while I understand the PQ (even if I may not agree with them), as an American I am mystified by the NDP/Liberal split.  It really seems like an accident of history to me, and I am surprised it hasn’t been crushed by the exact forces that are described in the video.  But the fact is it hasn’t.  The party faithful of those two parties have a tremendous reservoirs of bad feeling for each other, it seems, and until those reservoirs run dry they will continue to oppose each other even at what seems like a high cost to the cause of the left as a whole in Canadian politics.

Possibly, although it is still going against what the principle of one vote one value means, which is a reaction to earlier voting systems which gave extra votes to landowners or those who paid higher tax bills, for example. This isn’t the issue in your German example since each voter’s vote is of equal value to all other voters.

In particular, between states 1 and 2, “AB” increase their preference of “c” over “b” from 2 to 4 points; meanwhile “CDE” decrease their preference of “b” over “c” from 4 to 2 points. There is no change in *ordering* between states 1 and 2, but there is a substantial change in *intensity of preferences*. So, of course this is a huge improvement for “c” over “b”.

Whether or not Arrow’s impossibility theorem applies to range voting depends on the exact formulation; notably, the Wikipedia article says it doesn’t. (See the subsection on cardinal voting.) I misunderstood your original comment when I first posted, and I was going by the version of Arrow’s impossibility theorem on Wikipedia.

It’s my understanding that Arrow started by ignoring range voting, hence the theorem doesn’t apply. For what it’s worth, I have exactly zero interest in arguing over how to “properly” apply the theorem to range voting, though I think your generalization is perfectly reasonable.

Anyway, again, your original comment is correct. (I dropped the “technically” for you as a compromise!) I just wanted to give readers something to think about.

Consider the following two conditions of five voters ABCDE voting on the three candidates abc, using either unrestricted or restricted range voting:

State 1
  a  b  c
A 1  3  5
B 1  3  5
C 3  5  1
D 3  5  1
E 3  5  1
tl11 21 13
Ranking bca

State 2
  a  b  c
A 3  1  5
B 3  1  5
C 5  3  1
D 5  3  1
E 5  3  1
tl21 11 13
ranking acb

Nobody’s preference changed with regard to their relative preference of c and b (AB prefer c to b, CDE prefer b to c) nor did anyone change on the relative merits of a and c. Yet the overall totals changed from b>c>a to a>c>b.

Arrow’s impossibility theorem can be avoided using range voting (aka score voting). The idea is to score candidates like books on Amazon or athletes in the Olympics, and the candidate with the highest average score wins.

In your last line, you seem to be referring to the
Gibbard–Satterthwaite theorem. It is true that no voting system is completely immune to tactical voting, but, range voting does much better than other voting systems. In particular, you can always safely give your favorite candidate the max score and basically always give your least favorite front-runner the lowest score. As a result, range voting can handle a 3-way election very well. Even if you have 4 or more front-runners, I think range voting is still clearly better than any other system.

Anyway, I’ve spent several years studying voting systems as a hobby. My conclusion is that, for offices like president and governor, range voting (or some variant, like approval voting with a top-two runoff) is the only method that makes sense. Range voting would also be a huge improvement for legislative seats, though I think using a combination of proportional elections and citizen’s juries would be better still.

In general, those criteria are:
No one individual controls the entire election.
It must always be able to rank every option, and those rankings must be deterministic on the voting.
The preference of the people for owl over tiger and gorilla must not change the relative ranking of tiger and gorilla. (This is the major problem with FPTP) (Independence of irrelevant alternatives)
If everyone prefers one option to another, the preferred option must win.

This doesn’t hinge on the difficulty of breaking ties, either: The proof is that there is somebody who can manipulate any system with the last three qualities to control the entire decision.

However, it is objectively not true that first past the post leads to a two party system.  Canada is the obvious exception, with four major parties.  There are two parties that would be the normal two parties in many other countries (Conservatives and Liberals), one party that exists due to regional concerns that trump the basic left/right spectrum (Parti Quebecois), and one party that exists due to, as far as this American expatriate in Canada can tell, an accident of history caused by some VERY hard feelings (the NDP). 

This leads me to conclude that two parties are inevitable only if the preponderance of the issues that drive how people vote can be arranged roughly on a single dimension.  If there are two or more dimensions involved (regional animosities, historical grudges, etc.), two parties are not inevitable. 

Needless to say, though, “one person, one vote” need not have anything at all to do with FPTP.