[xvedejas]

What would you say to someone like me who feels that IRV is perhaps the worst possible alternative voting system to advocate for? It feels like someone at some stage must be very dishonest, or otherwise dangerously uninformed, to think that IRV is worth advocating for over alternatives like approval voting, range voting, or any Condorcet voting system. I'm very worried that most places will have the political will to improve the voting system only once in a century and we'll have wasted it on a system that's unusually ill-behaved. I'm particularly concerned about IRV's non-monotonicity, whereby it's possible to hurt a candidate by ranking them higher, and likewise it's possible to help a candidate by ranking them lower. How can anyone feel they're voting honestly in an honest election when this is the case?

[klodolph]

Two reasons: Arrow’s impossibility theorem and the fact that people are not perfect logicians.

I honestly thought that after learning Arrow’s impossibility theorem that Condorcet is not especially important. Since we can’t have a perfect voting system, we have to pick an imperfect one, and among the alternatives, it’s important to capture information from voters. Instant runoff captures a lot of information.

Approval voting I think is much too tactical and, strictly speaking, worse than IRV. No contest.

IRV lets people express their preferences in a fairly understandable way. The strategy I see people talking about is “rank all the front-runners, and use the leftover spots to rank the people you want to win, even if they’re not likely to win.”

So if A B C and D are front-runners, and E and F are the two other candidates you like, you come up with a ranking for those six and put the top five on your ballot.

The idea that people who like this system are “dangerously misinformed” or “dishonest” is needlessly inflammatory.

[godelski]

> Arrow’s impossibility theorem

First off, Arrow's doesn't apply to all systems. You'll need to look into both Gibbard's and Gibbard-Satterthwaite's theorems.

Second off, just because you can't find a global optimization in a highly dimensional space doesn't mean there aren't local optimizations along criteria we care more about. Appealing to Arrow's is a cop-out.

> Approval voting I think is much too tactical and, strictly speaking, worse than IRV. No contest.

You're going to have to back this up with some strong evidence. Approval has higher VSE, is simpler, is more resistant to spoilers and tactical voting.

> IRV lets people express their preferences in a fairly understandable way.

Actually your argument holds true for any ordinal or cardinal system. Cardinal even having more flexibility since you can give two candidates the same score. And in cardinal if you want to rank your candidates, no problem. Better yet, you have better encoding opportunities because you can specify the distance between your ranking instead of the uniform spacing that ordinal systems force upon you. (BTW, given what the person above you wrote, I would assume that they know how ranked voting works and explaining how it is going to come off as you calling them dumb).

[magila]

One big problem with approval voting is that it presents voters with a difficult conundrum: what do you do with candidates you don't particularly like but would still strongly prefer over one-or-more other candidates? If people are too lenient with their approval it increases the risk of someone no one really likes getting elected over someone a majority would have preferred. If people are too stringent you start running into the same problems as FTTP.

Approval voting has some nice mathematical properties, but I think in practice trying to pidgeon hole people's preferences into a binary decision would be a major source of voter frustration and lead to tactical voting.

[godelski]

Fine, go STAR or Score/Range. Honestly I prefer those systems (in that order and I'd argue most people that are pro cardinal systems have that same preference[0]). Nice benefit is that people can bullet vote and we collapse to Approval which is a "good enough" system.

> but would still strongly prefer over one-or-more other candidates?

In fact, this is why I argue for STAR or score. It encodes information for better than a ranked (ordinal) system. In any ranked system you encode your preference with equidistant from one another. Where as when you score you can indicate a much stronger preference.

Here's an example. Let's say I REALLY like candidate A, moderately like candidate B, and strongly dislike candidate C.

Ranked:

A > B > C (with my encoding I'm saying that my preference of A over B is the same as my preference of B over C)

Scoring

A: 10, B: 7, C:0 (with this encoding I can indicate that my preference of A over B is not as large as my preference of B over C. Obviously we are capturing more information here)

Let's just encode information better, I agree. But also let's consider other factors like how easy it is to count the votes (which every cardinal system is going to beat ranked systems).

[0] That same preference where the distance between STAR, Score, and Approval is smaller than the distance between preference of Approval over IRV (e.g. STAR: 10, Score: 8, Approval: 7, IRV: 3, Plurality: 0).

[ad8e]

Small correction: The term "bullet voting" means voting for one candidate only (001000), rather than voting 0 or 1 on each candidate (101011). It is caused by low engagement from the voters, who only take the time to learn about one candidate, their favorite. It has been a problem for approval voting in practice, and it is unclear to what extent it affects score methods in practice.

I think STAR is slightly worse than Score, is comparable to Approval, is much better than IRV, and is likely better than Condorcet methods. STAR has some odd behavior which can be explored in a 3-person race. Score has less-problematic behavior caused by risk-taking with equilibrium voters (not like voters behave in any way similar to Nash equilibria though, and who knows what the real-world behavior will be).

However, STAR's main benefit may be in overcoming political resistance, if its properties are simpler to convince voters. Majority criterion sounds nice even when it is inefficient. Much like Top Trading Cycles losing to Gale-Shapley in school choice algorithms (excluding Boston).

[ClayShentrup]

There is absolutely no evidence that bullet voting has been a problem with approval voting.

https://www.rangevoting.org/BulletBugaboo.html

> I think STAR is slightly worse than Score

I would say they are probably roughly equal, but the best computer modeling we have shows that star tends to perform a little better.

https://electionscience.github.io/vse-sim/VSEbasic/

> However, STAR's main benefit may be in overcoming political resistance, if its properties are simpler to convince voters. Majority criterion sounds nice even when it is inefficient.

You're definitely correct on this.

[ClayShentrup]

1. Extensive game theoretical analysis, and even computer modeling, has shown that approval voting resists tactical behavior better than virtually any other voting method.

https://electionscience.org/library/tactical-voting-basics/

There's even an entire book focused on the game theory and tactics of voting methods, which advocates score voting, approval voting being score voting on a 0 to 1 binary scale.

https://electionscience.org/library/tactical-voting-basics/

Approval voting elections have been successfully held in 2020 and 2021 in Fargo in St Louis respectively, and there were no indications of voter confusion or anything like that.

https://electionscience.org/press-releases/st-louis-voters-u...

[klodolph]

I disagree that cardinal voting is understandable. It’s how we rate restaurants and review products on Amazon, and I don’t think it translates to an election with multiple options.

The issue here is not just how logical humans “homo economicus” behaves, but how actual voters behave.

Not really interested in engaging with the rest of this comment right now, but suffice it to say that I don’t think you’re accounting for human behavior in practice, which is messy and illogical. I don’t think it’s reasonable to say that I’m appealing to Arrow’s impossibility theorem as a cop-out—I’m saying that since we don’t have a game theoretic solution the the problem, we should look at the actual behavior of imperfect, irrational humans as the deciding factor.

[godelski]

> I disagree that cardinal voting is understandable. It’s how we rate restaurants and review products on Amazon, and I don’t think it translates to an election with multiple options.

I disagree but also don't see this as a problem. If you rank candidates you still get the majority of the desirable properties. Rank with non-equal distances, even better. Hell, it isn't even bad if you bullet vote (that's just approval voting). Investigating non-optimal ways of voting under any voting system is an extremely important analysis. So for the voter there is no problem. I'm also kinda put off that you give real world examples of humans using cardinal methods and then claiming that we can't understand it (HN is using cardinal voting...)

But we also have to consider the counting of votes side of "understandable." Plurality is pretty damn easy, and this is clearly why we use it. Approval is almost as easy (just just sum multiple columns). Range/Score isn't much harder. Then STAR introduces 2 rounds of counting. Then we look at IRV and we see that we have tons of rounds. This isn't typically so bad in a presidential election where there are realistically about 4 candidates, but that complexity increases real fast elsewhere. Just watch NYC. There's going to be at least 5 rounds (probably more). This is far more complex. We only have to look at Arizona to understand why this part of the "understandable" question is important.

[justinpombrio]

For anyone like me who hadn't heard of Gibbard's theorem, it's actually even simpler (and more depressing) than Arrow's theorem. To quote Wikipedia:

For any deterministic process of collective decision, at least one of the following three properties must hold:

1. The process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome;

2. The process limits the possible outcomes to two options only;

3. The process is open to strategic voting: once an agent has identified their preferences, it is possible that they have no action at their disposal that best defends these preferences irrespective of the other agents' actions.

https://en.wikipedia.org/wiki/Gibbard%27s_theorem

----

So basically, it's impossible to completely eliminate strategic voting. No matter the method: ranked vs. cardinal vs. anything else you dream up can't help.

[godelski]

> it's impossible to completely eliminate strategic voting. No matter the method: ranked vs. cardinal vs. anything else you dream up can't help.

I think this comment is a defeatist at best and deceitful at worst. Just because there is no global optimization does not mean that all optima are equal. We can in fact have optima that are better than one another (including all optima we know about!). This is a common feature of highly dimensional solution spaces.

The big issue here is that not all criteria are weighted equally, by desire of effectiveness. So we find an optima where we optimize features that have a large weights and care less about optimizing features with small weights. By doing this we can compare systems in their desirability and select the best ones. This is not cause for throwing up your hands and giving up.

As an example: cardinal systems, when compared to ordinal (ranked) systems, are more resilient to strategic voting and simpler (both for the voter and for the people tallying the votes, aka transparency). The cost? Slight decrease in maximal VSE. BUT if we look at the min, mean, median, or modes of VSE given different strategies cardinal system outperform ordinal (aka, desirable). You can see this by comparing with this chart[0]. For example with STAR0-10 we have maximal VSE of .983 and minimal of .912 (actually this makes it strictly better than plurality!). But if we look at our best ordian, RP, we see RP has a maximal VSE of .988 and minimal of .870. So on terms of maximal there's a 0.005 difference but on minimal there's a difference of 0.042! We can easily tell here that STAR is much more resistant to strategic voting than RP (Shulze is even worse!). Doing the same for IRV we see .07/.115 (max/min comparison of STAR0-10 vs IRV on VSE).

So we can compare. We can select better methods. But is there a ''perfect,, solution? No. But don't let the lack of the ability to create a perfect system detract from the ability to compare systems. Not all is lost.

[0] https://electionscience.github.io/vse-sim/vse.html

[justinpombrio]

> I think this comment is a defeatist at best and deceitful at worst.

Wow, very HN! I don't actually mind very much, but seriously, consider applying the principle of charity?

I agree with you, and did before you wrote this comment too! Hence my use of the word "completely". I was just surprised that strategic voting couldn't be completely eliminated; before yesterday I expected that you could, in exchange for losing other nice properties. Of course being impossible to eliminate completely doesn't mean it shouldn't be minimized.

[pksebben]

according to Wikipedia:

>Gibbard's theorem states that a deterministic process of collective decision cannot be straightforward, except possibly in two cases: if there is a distinguished agent who has a dictatorial power, or if the process limits the outcome to two possible options only.

.. it also mentions that gibbard's is specifically about irv.

All that aside, I can't understand the idea that we only get to change things once. My understanding of history is at odds with the concept.

[justinpombrio]

> .. it also mentions that gibbard's is specifically about irv.

No, Gibbard's is not limited to any particular voting method. I think you're misreading the next paragraph (and also confusing IRV, which is a particular method, with ranked choice, which is a whole category of methods). Note the distinction between Gibbard and Gibbard-Satterthwaite:

> A corollary of this theorem is Gibbard–Satterthwaite theorem about voting rules. The main difference between the two is that Gibbard–Satterthwaite theorem is limited to ranked (ordinal) voting rules: a voter's action consists in giving a preference ranking over the available options. Gibbard's theorem is more general and considers processes of collective decision that may not be ordinal: for example, voting systems where voters assign grades to candidates.

[godelski]

> it also mentions that gibbard's is specifically about irv.

This isn't true

> I can't understand the idea that we only get to change things once.

Those of us concerned about IRV and promoting cardionality actually looked at history. Between 1910 and 1920 40 US cities used Bucklin voting (similar to IRV, slightly better even) and all repealed them[0]. So looking at history we see that people recognized the need for a better voting system, implemented something similar to IRV, saw that it didn't make things better, and subsequently said "fuck it, we'll go back to FPTP because it is easier." (I should also mention that in Australia, since 1949, 90% of Lower House elections, which use IRV, are equivalent to using FPTP[1])

So we're looking at history (and modern times) and saying "hey, this didn't work and actually ended up causing us to take a step backwards. Maybe we shouldn't repeat the same mistake."

I hope this clarifies our differing understanding of history.

[0] https://clayshentrup.medium.com/momentum-e5fd12ffce2a

[1] https://en.wikipedia.org/wiki/Australian_House_of_Representa...

[pksebben]

A little, I think we may have different ideas about what the difficulties were in the early 1900s vs now - I believe that the circumstances are different enough now that broad conclusions about what is and isn't feasible cannot be drawn, but that's just a piece of the puzzle and I think your point deserves merit.

What I would ask, then, is rather than not doing IRV, what should we do, in your opinion?

I'm looking at this as a sort of crisis situation, as our ability to affect our politics is in a state of constant erosion, and the process of capture at work here can only end in systemic collapse - the further power gets concentrated, the more centralized our decision making becomes, and the more vulnerable we become to systemic single point of failure.

I would love to see STAR voting become a thing. I think of IRV in the current context as a proof-of-concept that might show people that we can change the structure of voting. I can't see anyone wanting to go back to FPTP, because I don't really see anyone who thinks it's even remotely working.

[logicchop]

> Cardinal even having more flexibility

I thought Gibbard-Satterthwaite (or maybe just Gibbard's version) applied to cardinal systems as well. This seemed likely to me for some reason, as if an ordinal method could approximate any particular cardinal discretization by just including "ghost" candidates that can be packed (ordinally) between your actual candidates.

[godelski]

> I thought Gibbard-Satterthwaite (or maybe just Gibbard's version) applied to cardinal systems as well.

Correct, but it is also a weaker version of Arrow's (also as Clay points out, Arrow's isn't really about voting[0]...)

> This seemed likely to me for some reason, as if an ordinal method could approximate any particular cardinal discretization by just including "ghost" candidates that can be packed (ordinally) between your actual candidates.

Okay, but this just adds complexity. Cardinal is already simpler than ordinal systems (both for voters _and_ for those counting the votes). There's absolutely nothing wrong ranking candidates in a cardinal system (it's actually pretty unlikely that you'll have the same preference for multiple candidates so this is going to naturally happen). The difference? In cardinal you can better express your preference of one candidate over another (I give an example here[1]). So now we've added "encoding efficiency" to the added benefit of cardinal systems.

Cardinal systems are better than ordinal systems in almost every single way (the only thing I can think of ordinal systems doing better at is that RP and Schulze perform better on maximal VSE, but as I discuss here[2] that is pretty limited as well as unlikely considering strategic voting and the ability to manipulate people exists).

[0] https://news.ycombinator.com/item?id=27598975

[1] https://news.ycombinator.com/item?id=27599324

[2] https://news.ycombinator.com/item?id=27600248

[jeff_tyrrill]

I wouldn't choose to use the word "dishonest" but I sympathize - in nearly all news media explanations of "ranked choice voting", the description solely explains instant runoff, and makes no mention whatsoever that there is a choice of algorithm that comes with the choice to use ranked ballots, such as Condorcet. The words "instant runoff" are almost never mentioned.

Choice of language matters, and "ranked choice voting" (to solely mean "instant runoff voting") is a conceptually misleading term meant to load the debate. It dis-educates rather than educates on how voting systems work.

Advocates of other voting systems have to first start out by explaining this misdirection and unpacking the wrong mental model, then get to the merits of one voting system vs. another - because people have been told that "ranked choice voting" works a certain way and only a certain way.

[klodolph]

I’d say that part of the cost of switching voting systems is educating voters how the new system works. Many voters simply don’t care about the finer details and just have a couple desiderata—we want to have our vote count, and we want to be able to vote for our favorite candidate.

Instant runoff is super easy to explain and achieves those desiderata, at least to some extent.

It’s hard to quantify the differences in mathematical terms against soft concerns like “we can educate voters and explain how this system works”. For that reason, I would like to see a non-mathematical argument against IRV, one that accounts for the other half of the voting problem.

[godelski]

> Instant runoff is super easy to explain and achieves those desiderata, at least to some extent.

Except IRV doesn't. Not only are cardinal systems easier but IRV doesn't achieve the most desired feature that people are looking for: no spoilers (or alternatively put, allowing votes for 3rd parties without "wasting" your vote). In fact IRV increases spoilage while cardinal systems (which is alternatively proposed) decreases[0]. Meaning we're doing the opposite of what we're trying to accomplish.

As for simpler, I'll refer you to this[1]. The short story is just rate candidates. And if you end up ranking, no worries. It's more difficult to mess up.

[0] https://www.rangevoting.org/SPRates.html

[1] https://medium.com/election-science/star-voting-is-simpler-t...

[abecedarius]

I'm always baffled by this claim that simple explanations favor instant runoff.

Here's approval voting: "Upvote the candidates you like. The candidate with the most total votes wins." It's not just mathematically simpler, it's simpler in informal terms, a smaller change from current plurality voting, and it seems less messy in the strategic dynamics insofar as we've tested these different systems for real.

[godelski]

Even score voting is easier than IRV. You can rank if you want to. But you can better specify preference because you're not ranking with the same preferential distance between candidates and people. We use score all over the place (we could call Hacker News score voting with a small range: -1/0/+1).

[ClayShentrup]

But there's no point in Condorcet because score voting, STAR voting, and approval voting have superior performance and are simpler.

https://www.rangevoting.org/CondorcetExec.html

[ClayShentrup]

> Approval voting I think is much too tactical and, strictly speaking, worse than IRV.

On the contrary, approval voting gets better results than IRV with any measure of strategic or honest voters. See extensive computer simulation results by Harvard stats PhD and voting methods expert Jameson Quinn. Brown (50/50) is probably the most realistic setting.

https://rpubs.com/Jameson-Quinn/VSE5key

A simple example of IRV strategy is next year's Alaska senate race. Murkowski would beat either rival head-to-head but is likely to be eliminated based on first-place votes. So Democrats want to strategically rank Murkowski 1st in order to help her survive to beat Tshibaka (Trump Republican) so they at least get their lesser evil.

Here's a good comparison of approval voting vs. IRV by experts. Full disclosure, I was a CES co-founder and have written extensively on this topic for 15 years.

https://electionscience.org/library/approval-voting-versus-i...

> I honestly thought that after learning Arrow’s impossibility theorem that Condorcet is not especially important.

I've visited Kenneth Arrow at his home and co-founded a non-profit that interviewed him. His theorem only applies to social welfare functions, not voting methods, if properly understood. But if anything, the moral is to AVOID ranked voting methods and instead use rated voting methods.

https://www.rangevoting.org/ArrowThm

[cosmojg]

For those who want to better understand VSE simulations and those who want to compare even more voting methods, see: http://electionscience.github.io/vse-sim/VSE/

[godelski]

Or if you want to see an animated version narrated by the gp of this comment (Clay) see this: https://www.youtube.com/watch?v=-4FXLQoLDBA

[asdfaoeu]

> On the contrary, approval voting gets better results than IRV with any measure of strategic or honest voters. See extensive computer simulation results by Harvard stats PhD and voting methods expert Jameson Quinn. Brown (50/50) is probably the most realistic setting.

If you look at the graph with the honest strategy you get better results with IRV which is basically his point.

[godelski]

We shouldn't assume 100% honest strategy in reality. It is an idealistic metric. It's not practical since people aren't 100% informed. Nor should we only consider optimal strategy. We need to consider the max, min, and median to determine robustness and better estimate real world results. Both the max and min for Approval is better than the max and min of IRV (in other words, the range is smaller and the expected result is more representative).

[logicchop]

> IRV lets people express their preferences in a fairly understandable way. The strategy I see...

That's the concern though. You likely don't want to just "express your preferences." You need to strategically rank candidates. But then what are you being asked to do exactly when you go to vote? I don't think it would fly if the instructions on the ballot gave you guidance on how to "strategize" your rankings. But if it doesn't give that guidance, it's misleading.

And I understand that all voting mechanisms have their own unique pitfalls; so we have to fall back to pragmatic questions. And one major pragmatic question is: What's the status-quo/What is everyone already accustomed to? Asking a large voting body to switch methods is not easy and I think it's being motivated largely by a misleading "grass-is-greener" claim about rank voting.

[caf]

The non-monotonicity tactical voting possibility is overblown: it only really works in the toy "which is the favourite pizza of these 30 students" examples.

In real world elections, the conditions where it is even theoretically possible arise only rarely (A > B > C with three choices, but B > A and A > C with two choices, and A's lead over B significantly greater than B's lead over C in the three choice scenario, and A's lead over C in the two choice scenario more than twice B's lead over C in the three choice scenario) and more importantly, they're not predictable enough beforehand. Advocating this kind of tactical vote stands at least as much chance of hurting your candidate as helping them, so nobody does it.

When you analyse real-world large scale IRV elections, you find that cases where the IRV winner isn't the Condorcet winner are rare, and this balances against the very real benefit of having a counting method that is easy to explain and understand.

[godelski]

The non-monotonicity is actually pretty important and we have real world examples of this. Clay mentions the Alaska race in this comment[0]. We've seen this issue in Southern states that used this to disadvantage black voters. This is also the reason Bernie would spoil Biden (and vise versa). So I'm not sure what you're getting at.

[0] https://news.ycombinator.com/item?id=27598975

[caf]

Let's look at the "Bernie would spoil Biden" example.

The idea is that the Republicans endorse only one candidate, Trump, and the Democrats endorse two: Bernie and Biden. In the non-tactical voting case, the second-last round votes shake out like:

  Trump 45
  Biden 28
  Bernie 27

Bernie is eliminated, the votes in his pile split 24 / 3 between Biden and Trump (a preference flow of 89% to Biden) and the final round of counting ends up:

  Biden 52%
  Trump 48%

..but tactical voting intervenes! A small number of Trump voters (2% of the total electorate) are organised to tactically switch their votes to 1. Bernie 2. Trump, resulting in a second-last round of:

  Trump 43
  Bernie 29
  Biden 28

Now Biden is eliminated, the votes in his pile split 20 / 8 Bernie/Trump (a weaker preference flow of 71% to Bernie, because of Biden voters too conservative to vote for Bernie) and the final round is now:

  Trump 51
  Bernie 49

Tactical voting has won the day!

However, this really illustrates the problems here for the prospective tactical voter:

1. They need pretty perfect information to pull this off. Not just on first round votes, but on how the preferences are going to flow as well. If those Biden votes flowed a little weaker to Trump, all they'd have done is elect Bernie instead; if Trump had been a little stronger overall than they expected in the no-tactical-voting, their tactical voting attempt might have backfired completely and turned a fair Trump win into a loss! Opinion polling just isn't this precise.

2. They have a co-ordination problem. If they switch too few votes, the scheme fails and they just elect Biden with a greater margin than before; too many and the scheme fails and they elect Bernie, a candidate they're presumably less happy with actually getting the Presidency than Biden.

3. All of this only works if the balls line up perfectly in the first place, even setting aside the problem already mentioned of how you know the balls are going to line up. If the second-last round votes are instead Trump 45 / Biden 30 / Bernie 25 then the Bernie to Biden preference flow has to fall under 66% for the scheme to be possible.

Rather than trying to engage in this dubious and risky tactical voting attempt, the Trump campaign would be far better served just spending their resources trying to turn out more of their voters. After all, the theoretical possibility only exists when the margins are tight in the first place.

A tangential matter is that even in an IRV election it still probably makes sense for the parties to either endorse only a single candidate each - otherwise their candidates will waste some of their resources attacking their co-party candidate when they could have launched them against their main opposition - or at least mutually agree to distribute campaigning material advising to give a second preference to their co-party candidate (a so-called "preference swap" arrangement).

[throw5away]

Honestly IRV is _even worse than plurality_. It doesn't solve the problems it sets out to solve (it entrenches two-party domination [1]), it has ridiculous monotonicity violations [2], all for a lot more complication in counting the votes (you can't distribute the counting well without transmitting the contents of all of the ballots) and possibly wrecking the secret ballot (you can encode and buy specific down-ballot rankings).

Seriously, it's all of the disadvantages and very limited upside.

[1] https://rangevoting.org/TarrIrvSumm.html [2] http://zesty.ca/voting/sim/

[zestyping]

And worse: it suppresses the Black vote, as if we didn't have enough of that already.

https://rangevoting.org/SPRates.html

https://www.yes2repeal.org/spoiled-ballots

IRV means much higher rates of spoiled ballots, disproportionately in low-income neighbourhoods. It's actively harmful.

[wslack]

> you can't distribute the counting well without transmitting the contents of all of the ballots

There are only so many combinations of rankings that are possible. It shouldn't be hard to encode each of those possible orders and transmit them as a whole.

[godelski]

> There are only so many combinations of rankings that are possible.

O(n^2) isn't great though...

The algorithm to count is rough and requires many rounds (since you count, knock out the lowest candidate, recount, and repeat until a >50% favor is achieved by one candidate). Cardinal systems on the other hand just require summing the columns and taking argmax. This is far simpler (in fact we can do most of this in parallel making a far better runtime).

[zestyping]

"Only so many" = At least N factorial. If ties are allowed, then even more.

With 20 candidates in an election, that's over 2 billion billion possibilities. It's not practical.