Here in Australia you number the box next to the candidates name from 1 to N this is not normally an issue for the local seat in the lower chamber (house of representatives) where there are a manageable number of candidates, but in the upper chamber where senators are elected on a state wide basis you end up with sometimes farcical situations like the infamous "tablecloth ballot paper" which had 264 candidates.
There has been some attempt to reform this such as forcing people/party's to pay a registration fee in order to appear on the ballot (this is done to cut down on so called nuisance candidates but it is arguably undemocratic, although I believe you are eligible for a refund of the fee if you poll above some threshold % of votes which is a fair compromise in my opinion).
It's not enough (£500 currently) to be a meaningful expense to any candidate actually trying to win, but it's enough friction for 'fun' campaigns that we get enough to be funny but not enough to really interfere with anything.
And, yeah, ours is called a deposit because if you get 5% of the vote you get it back - and the phrase "lost their deposit" to reference a candidate who thought they were real utterly cratering on election day is pretty widely known.
Of course the UK's system of government is largely a patchwork of oddities that, put together, mostly work for us, so how well any particular oddity will work in another system is invariably debatable.
You could list the candidates in random order with a number next to them, and then have people write down those numbers in order. That, like anything else, would have failure modes, though.
An NxN matrix for N candidates allows using "marked or not" detection, but it creates a huge ballot even with just a handful of candidates.
Dowdall's method assigns 1, 1⁄2, 1⁄3... points to the 1st, 2nd, 3rd... candidates on each ballot, then elects the candidate with the most points. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives each one very different properties.
Ranked voting systems are usually contrasted with rated voting methods, which allow voters to indicate how strongly they support different candidates (e.g. on a scale from 0-10).[1] Rated voting systems use more information than ordinal ballots; as a result, they are not subject to many of the problems with ranked voting (including results like Arrow's theorem).
That's a bucket full of problems. I remember that I had a similar problems years ago when I wanted to consolidate several lists about the "daily usefulness" of Chinese characters. How much does it weigh when you put A, B, C in that order? is A=1/1, B=1/2, C=1/3? or maybe A=0, B=-1, C=-2? To quote the above, "Ranked voting systems vary dramatically in how preferences are tabulated and counted". This should be a red flag! I'm happy to see that alternatives to first-past-post are tried out in some locations such as Alaska, Maine and Australia, but why ranked voting?
Ranked voting is only good when you think of yourself as a sole, lonely voter. You put the candidates into this order: A, B, C. But there will be other voters with other preferences. Let's say you're three people and the rankings are ABCD, EBCD and FBCD. Now you have three favorites A, E, F that are preferred choices, and there's that also-ran B who only was second best. But B got three second-best votes whereas each of A, E, F only got one vote.
So answer my question: how many second, third, fourth votes will it take to surpass a given number of first votes? If there's another ballot in the same election with GCBD on it, now you have B with 3x2nd and 1x3rd place. You cannot add, subtract, multiply or divide these numbers. There's no clear answer (although practical procedures can and have been proposed and used) and that bugs me. The entire thing looks like a game of Bridge, Skat or Poker to me, full of justifiable but ultimately very arbitrary rules, hard to explain and tricky to get right. https://en.wikipedia.org/wiki/Condorcet_method says that much to me. One also has to account for unranked candidates and decide whether it should be possible to give one rank to several candidates, and then whether (as done in sports) the next rank must be left empty.
It just goes on and on, the list of options to do the ballot and to do the counting is truly mind boggling. This is the reason I've come to much prefer preference voting over ranked voting. Ranked voting is much too complicated for general use in a general election whereas preference voting is simple and clear and the number of "design choices" as it were is drastically reduced when compared to ranked voting.
The ordinary case of preference voting is extremely explainable: if more people prefer A to B than prefer B to A, A beats B; pick the candidate that beats everyone else. "It's like running a bunch of head-to-head elections all at once."
They're also really easy to tally into a table: "A ranked above B" is a point for A over B; "B ranked above A" is a point for B over A; A and B ranked equal relative to each other doesn't add anything to either of those two cells.
The corner cases like cycles almost never come up. And even then, it's relatively easy to explain a high-level understanding of the most common methods: "if there's a loop of people who each beat the next one in the loop, ignore the one with the smallest margin of victory". If A beats B in a landslide, B beats C in a landslide, and C very narrowly beats A, A wins.
Also:
> Let's say you're three people and the rankings are ABCD, EBCD and FBCD.
Every ballot implicitly ranks every option, and the usual assumption is that if someone doesn't even care enough to list a candidate, they prefer every candidate they did list over any candidate they didn't list. (There are UX design ideas that could let someone say "this candidate is last" without ordering every candidate, but that adds complexity.) So these ballots are:
A > B > C > D > E = F
E > B > C > D > A = F
F > B > C > D > A = E
Given especially US multi-race ballots, I find it a lot harder to see the incremental complexity of approval voting having a noticeable effect (though note for calibration that there's plenty of criticism out there for how confusing many multi-race ballots are as is).
I am concerned tho that preference voting (is that the right word?) gives people too many opportunities to screw up—there are too many things that can go wrong on the ballot (ones I've seen have three columns for 1st, 2nd, 3rd preference, and there should be at most? exactly? one mark in each column). Also vote counting has too many ifs and whens and seemingly arbitrary rules how my ballot will be counted in case my 1st choice doesn't clearly make it on first count.
Writing down candidates names will make for some fun days when it comes to counting. Plus, what if multiple candidates have similar names? And, a ballot with a scribbled "Miller!!1!" on it, do you mean Ms Annie Miller from Portland Oregon? That one? Lastly, when was the last time another person was able to read your scratches?