Is there a name for 1:1 preference-to-ballot response?

[u/Known-Jicama-7878]

In ordinal voting, there is only one ballot response to A>B>C...

• A = 1
• B = 2
• C = 3

In Range/Score voting, there can be multiple responses to A>B>C. Assuming a score range of "10" we could have...

• A = 5
• B = 3
• C = 2

Or

• A = 7
• B = 2
• C = 1

Is there a name for how ordinal voting only produces one possible ballot response? In other mathematics, we would call it "one-to-one correspondence", "bijective", "symmetric", or "isomorphic".

Is there a name for ballot types that elicit ballot responses that are exclusive to the preference of the voter (not counting indifferences)?

Thanks for any thoughts!

Edit: corrected ordered set operators to ">". Explicitly stated the score range was 10.

[u/DaraParsavand]

I have absolutely no idea what you’re asking and I have read a fair amount about voting theory and have taken graduate level math classes (though many years ago). Maybe you can edit your post to make your question clearer. Also, it appears you meant to write A>B>C which is how it is always written if A is someone’s first choice.

[u/Known-Jicama-7878 → u/DaraParsavand]

Thanks for the reply! They have been fixed.

[u/rb-j]

In ordinal voting, there is only one ballot response to A≺B≺C.

You need to correct this. You mean A>B>C . A is preferred to either B or C and B is preferred to C. Also, to be meaningful and to compare apples-to-apples, you need to settle on a fixed range for Score Voting. I suggest to stick to six scoring levels: 0 to 5 (unmarked is a score of 0), just to be consistent with STAR and most other Score Voting schemes. That said there comes a natural restriction in meaningfully mapping from ranked A>B>C. We assume that no voter wants to dilute their vote unnecessarily. That means A will always be scored 5 and C will always be scored 0.

The big question is how will B be scored? Any integer from 1 to 4.

Going from ordinal to cardinal is not a bijective mapping. It's not just the different scores (like if it were STAR), but this is true also for Approval Voting (which is a degenerative case of Score Voting with just two levels of scoring; 0 and 1).

A>B>C could map to Approval two meaningfully different ways:

• A=1
• B=1
• C=0

or

• A=1
• B=0
• C=0

And it comes down to the same tactical issue for voters as does Score Voting (or STAR) in the case of 3 (or more) candidates. How high should the voter score or Approve their 2^nd favorite candidate? Should they Approve their #2 or not? Should they score their second-fav with a 4? Or 3? Or 1?

That is the problem with cardinal systems. If there are 3 candidates or more (and this is precisely the case that motivates voting reforms over FPTP), they inherently require the voter to vote tactically the minute they step into the voting booth. This is why I do not plug Approval or STAR, myself.

You can see what the problem is for the voter if they score (or Approve) candidate B too high (it harms their vote for A) or too low (it harms their negative support for C).

I want everyone's vote to count equally. If you prefer Candidate A tepidly and I prefer Candidate B enthusiastically, your vote for A should count no less than my vote for B, if the election were to come down to a race between A and B as leading candidates.

The only way to do that is with the ranked ballot and a Condorcet-consistent method for tallying the ballots and determining the winner. Score Voting and Approval Voting miss that fundamental mark.

[u/Known-Jicama-7878 → u/rb-j]

Hello,

Thanks for the reply!

You hit upon what I was attempting to convey: Score Voting has multiple compatible ballot responses for the same preference schedule, whereas ranked voting (what I called ordinal voting) does not.

Apologies in not saying it correctly and clearly.

Is there a name for this phenomenon of some voting systems having multiple ballot responses possible for the same voter preference schedule?

[u/rb-j → u/Known-Jicama-7878]

Is there a name for this phenomenon of some voting systems having multiple ballot responses possible for the same voter preference schedule?

I dunno a name. But this is inherently imposing the burden of tactical voting on the voter. Any cardinal method suffers that flaw whenever there are 3 or more candidates. The voter has to decide how high they're gonna score their 2^nd favorite (or lesser evil) candidate. But they don't have that problem with ranked-order ballots (as long as the method doesn't fuck them over and IRV has been known to do that).

[u/sleuthfoot]

Imagine the elderly trying to figure this out at the voting booth

[u/Known-Jicama-7878 → u/sleuthfoot]

Plenty of states already have a ranked choice ballot of some kind. Even kindergartners can put a “1” on their favorite option, and put a “2” on their second favorite if they do desire, etc.

The concerns about ballot complexity 10 years ago turned out to be overblown.