On the voting side it's simple: rank your choices. You have a first-choice favorite, a second favorite, a third favorite, and so on. If that's all you know, you can vote and do okay.
Counting votes is a little more complicated. There's more than one way to do it. The two ways offered here are Virtual Round Robin and Instant Runoff Normalized Ratings.
In a round robin tournament, every competitor goes up against every other competitor. Applying that to an election, the question is how many people like choice A better than choice B, and how many people like B better than A. If more people prefer A over B, A should win.
When you rank your choices, you say that you prefer your first choice over your second choice, and your second choice over your third choice. You also implicitly say that you like your first choice over your third choice. You have expressed a preference about every pair of choices that you have ranked on your ballot. Putting this together across all ballots and all competing choices we can say that more people prefer A to B, A to C, and so on.
It is rare but possible to have a situation where A beats B, B beats C, and C beats A. This is resolved by breaking the tie at the weakest match up. If A beats B by 60 to 40; B beats C by 56 to 44; and C beats A by 52 to 48; then we can discount C beating A and declare A the winner.
nstant Runoff Normalized Ratings (IRNR) starts with ratings ballots (on a scale from 0 to 10 where 10 is best, or some other scale). You can rate the choices however you like, give 10 to three choices, 4 to some and 0 to the rest; or any other set of values. Your vote is then normalized so that every vote has the same power. A ballot with five choices rated at 10 and five choices rated at 0 would have a different amount of power than a ballot with five choices rated at 1 and five choices rated at 0; normalization fixes this. All the normalized votes are added up. If there are more than two choices then the choice with the lowest sum is disqualified. All the votes are now re-normalized as if the disqualified choices were not on the ballot. If I had voted [10, 6, 3, 0] for some choices, but my first choice was my kinda fringe favorite candidate who got knocked out, my ballot [__, 6, 3, 0] would get re-normalized so that it still had full power, effectively giving a 10 rating to my second choice and scaling the rest of my ratings appropriately. In this way IRNR allows me to express myself in a very flexible way about all the available choices, and my vote is always represented with full power throughout the process.
Virtual Round Robin
IRNR is a somewhat esoteric method, only invented within the last few years. Virtual Round Robin (VRR) elections were invented over 100 years ago by a French mathematician named Condorcet and the method has had a great deal of study and is believed to be quite reliable and consistently good. IRNR requires a modern computer to count. VRR can be readily hand counted. IRNR has been shown to have slightly better outcomes than VRR in some scenarios of simulated elections.
Instant Runoff Voting (IRV) is a simple and easy to understand election algorithm that gets bad results. It was enacted in 2005 for the election of mayor in Burlington, Vermont. In 2009, on its second application there, Instant Runoff Voting elected the wrong mayor for Burlington, Vermont; and then it was repealed.
Let’s not make the same mistake. Better election algorithms are known, use those instead.