Of all the electoral systems that have been in wide use and documented, none are exactly like what you proposed. By the way, according to that Wikipedia page, "the study of formally defined electoral methods is called social choice theory or voting theory, and this study can take place within the field of political science, economics, or mathematics, and specifically within the subfields of game theory and mechanism design."
people vote for their favourite candidate and against their least favourite. The against votes are subtracted from the for votes.
First of all, "least favourite" does not explicitly mean "against."
If that's all there is to your proposed electoral system, then, to clarify, you're saying voters are required to make two, and only two, marks or voice-votes for a race: one mark denoting their favorite and one mark denoting their least favorite. It means either the amount of candidates has been restricted to two or that the voter is not allowed to vote for their "middle-weight" candidates about whom they feel more ambivalent. It's different from all presently notable voting systems.
Instant-runoff voting, known in the United States as ranked-choice voting and asserted by two of the answers previously offered to you that have at present the two highest numbers of approval votes from registrants to this website, is not what you proposed. In that system, the amount of marks may be optional, full (every candidate requires a mark), or partial (N marks, where N is less than the amount of candidates on the ballot for that race). Voters mark numbers denoting their rank of preference for the candidates. For all amounts of marks except full preferential, marks represent only approval. Marks never explicitly represent opposition or disapproval of candidates that the voter ranks lower. Further, its counting method is entirely different.
In approval voting, described by the previously offered answer that has at present the third-highest number of approval votes from registrants, marks represent approval and are decided for each candidate individually, not in ranking or comparison to other candidates. Some ballots for this system may ask voters to mark "No," which represents, "I do not explicitly approve." A blank or "No" does not explicitly represent opposition or disapproval because the counting and calculation method used by this system recognizes only marks of approval.
So beyond variables that precede these such as who is allowed to vote and how difficult it is to be allowed, there are variables in the format and layout of the ballot; variables in the amount, representation, and meaning of marks or blanks; and variables in the method and verifiability of... recognition, counting, and calculation.
As far as mathematical criteria, you can find most of them on Wikipedia's comparison of electoral systems. tl;dr: Jump down to the first table, or click the "Comparisons" heading. In my opinion, this is the best place to start of all the information I've read.
Two of the criteria for electoral systems that are often overlooked but I think are very important with the rise of voting machines are polynomial time and summability. In the context of electoral systems, polynomial time and summability basically tell you whether counting and verification by recounting can be done through a distributed method ($O(n)$) by each tier of polling districts verifying their district... or that counting and verification can be done only at one top-most central location ($O(n^m)$) to which is shipped every marked ballot or a copy of data from every ballot cast in the election. The location could be a warehouse filled with the marked ballots or a mainframe computer storing a database file.
Instant-runoff (ranked-choice) can be counted only at one top-most central location. If IRV was counted by hand and not by machines, a central location could allow better oversight than a distributed count, but ballots are not usually counted by hand anymore. They're counted by profit-influenced, proprietary, closed-source software on black-box hardware. Campaign officials, scrutineers, polling place volunteers, and most election officials are not known for being skilled in information security, cryptography, computer engineering, or software engineering. There are a few skilled ones who regularly consult to a national government, the United States, at the Brennan Center for Justice.
Another system similar to your proposal is score voting. Score voting that's been reduced to a three-point scale (approve, neutral, oppose) is used by Wikimedia's Board of Trustees and by the United Nations to select the UN Secretary-General. However, its marks are decided for each individual candidate, not explicitly in comparison to other candidates as your proposal is.
One more notable system, Schulze method, is used by ICANN, many free and open-source software projects, the Pirate Party in many countries, and the self-governing bodies of several languages of Wikipedia. It's one of the few systems that satisfies most criteria, but it's one of the most complex in polynomial time.