If you think policy of parties and candidates should matter more than mere popularity, then the mathematically ideal systems for aggregating collective opinions on multiple issues simultaneously are called cardinal voting systems.
In these systems, the voter gives an independent nuanced strength of support for every option/candidate available. This information is then aggregated in some way to find the most representative option for all voters, instead of "the favorite of the largest faction" as it happens today.
Let's step back for a bit to understand what's going on in an election. Each candidate/party can be seen as an "ideological package", a collection of proposals and so on.
Since in cardinal voting all opinions each voter gave for each option are independent, the aggregate opinion of all voters on every option accurately reflects the priorities and any existing consensus between the voters, which are now emphasized.
For example, a candidate who campaigns strongly on an important consensus issue while being mostly indifferent about a minor polarizing issue will gain support due to the consensus.
Candidates who campaign on polarizing issues will only gain support from a fraction of the population who are vocal about some specific thing. Currently, these dominate our elections, but with cardinal voting systems they'd rarely gain enough support.
Since important consensus issues typically have over a majority of support, candidates who make a strong stance on these are more likely to be elected, representing a non-partisan and non-polarized issue on the large scale.
Since all supports are independent, these candidates will be able to gain support on each issue the voter cares about independently. This means the population's priorities are naturally emphasized.
Some systems that can do this are approval voting, score voting, STAR voting, 3-2-1 voting:
- Approval Voting: Voters vote by independently approving any number of candidates out of the ones available. Most approved candidate wins.
- Score Voting: Voters vote by independently scoring on a scale 0-9 each of the available candidates. Highest total/mean score wins.
- STAR Voting: Voters vote by independently scoring on a scale 0-9 each of the available candidates. From the top two rated ones, the one preferred (rated higher than the other) by a majority wins.
- 3-2-1 voting: Voters vote by independently grading each candidate as Good\OK\Bad. From the top 3 with the most "Good" grades, select the top 2 with the least "Bad" grades. From these two, the one preferred (graded better than the other) by a majority wins.
Ranked systems CANNOT do any of this as well as these I just listed because they are majoritarian, which means voters are forced to take sides between two or more candidates, instead of the candidates having to appeal to a broader portion of the population. In other words:
- Ranked systems have "voters taking sides with the candidates", since between any two candidates they inevitably need to fully support one and not support the other. Even if there is a clear consensus on an issue, this procedure will artificially split the population into two groups which will then act as if they favor their candidate's opinions, not the group's own. This artificially creates opposing factions and encourages candidates and voters to focus on their differences, instead of their agreements.
Cardinal systems have "candidates taking sides with the voters", since the support each candidate receives is completely independent from the other candidates. So a voter is never "taking sides" at all, they can fully support two candidates at the same time, if they wish. The candidate who appeals the most to the population as a whole* wins.
Effectively, any ranked comparison is what we call zero-sum: supporting a candidate means NOT supporting another. And that is the cause of all these problems, because by "splitting the votes" the system encourages candidates to avoid overlapping one another ideologically, as that may allow other candidates to take votes away from them. Sadly, the most popular ranked system being promoted, Instant-Runoff Voting AKA Ranked Choice Voting, is particularly bad at this because in every elimination step 100% of a voter's support goes to a single candidate out of many, so similar candidates are still taking votes away from each other and penalizing one another, risking elimination. This leads to many other problems.
But in general, the effect of this "avoiding ideological overlap" effect of ranked voting systems is that different issues get artificially coupled together, like gun control and gay marriage. There's absolutely no good reason for a correlation between the two, but the "take sides" approach enforced by preferential majority rule allows and encourages candidates and parties to pick and choose the divisive issues, and then use them in their campaigning to gather support via single-issue voters. This leads to voters approving an artificially constructed "ideological package", which rarely gets anything important done. Sounds familiar?
That being said, Condorcet voting systems are ranked and majoritarian, and can do it to a lesser extent. This works because they try to find the overlap between all potential majorities, and this overlap usually covers the consensus issues. But all of these are too complicated to be seriously considered for official adoption in elections.
In contrast, all cardinal systems can be explained in a sentence or two, like I did above. So they're pretty easy to explain, use and understand, and fundamentally address many of the issues we're facing today in our democracies worldwide.
People are also familiar to how rating scales work, so it's not an unfamiliar concept. But there's a very important distinction between something like score voting, where you rate candidates, and rating of products on Amazon for instance. During an election, you are comparing all available candidates as a whole set, and each voter is giving some opinion on every candidate. This means the scale is specifically related (or "calibrated") to that set of candidates and the population's opinions taken together. This is what makes cardinal voting work, and what makes the opinions of voters meaningful and comparable when taken together.
Contrast with product ratings: people don't buy one of each of the many products available, try them all, compare them, then rate them all together. They buy one and rate one, and only if they really like or really hate it. They don't have to express an opinion, as in voting. So there's no common context to compare different product ratings, and this is why product ratings are really noisy, and why one should be careful when comparing user ratings.
Another BIG unique advantage of cardinal voting systems is that the pre-election polls will also have to be changed to reflect the system itself. This has several great effects since the idea of "viability" won't exist anymore. Each candidate will appear on the polls with their own independent level of support, obtained by their own merits. Since people are more honest in these polls than in actual elections, these will be extremely useful now.
Candidates who grow a grassroots movement would gradually increase in support in the polls, reflecting that accurately, which in turn attracts more voters to check them out. This will happen to all candidates simultaneously, and each will eventually plateau on the level of support they deserve relative to the rest (there actually a few theorems about this!). In this way, the pre-election polls under cardinal systems will finally serve their purpose to inform the voters about candidates, not to coerce and misinform them as it happens today ("Don't waste your vote!", "Your candidate isn't viable!"). And most importantly: campaign donations/money in politics becomes much less powerful, because what matters is how people are getting interested in the candidates. The polls will be enough free-publicity to all those that truly deserve it.
The key lesson: the competitive element of elections should happen outside the voting booth, not within it. The ideas are ultimately what's competing here, not candidates or parties. We don't want to have partisan-based politics, we want policy-based politics.
The parties and candidates are just representing a collection of those ideas with a given priority. That's why multiple parties/candidates can and should be able to independently support similar ideas, and none should be penalized for doing so. The mathematical way to do that is to make the support each voter gives to a candidate be completely independent from what they give to the others. That is the defining feature of cardinal voting systems.