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I find that often when people are trying to understand an idea, they aren't taking it very seriously. Perhaps its how they learned in school, where the point was to retain enough to select an appropriate answer on a test. There is no attempt to get a deep understanding. They seem to aim for a superficial understanding. Enough to show familiarity with the concept, but no more.
In contrast to this approach is something I'll call productive understanding. The goal it to learn an idea in a way that you can use it successfully and productively in the future. It requires looking at new ideas in a particular way, with an eye on making them useful.
How do you make ideas useful? Aren't there lots of ideas that aren't particularly useful? For instance, say you learn about Instant Runoff Voting. It is a method of voting for candidates where you rank all of the candidates. When all of the votes are in, a formula is used to determine the winner. Each person's highest ranked candidate vote is added up. Instead of that selecting the winner, the last place candidate is eliminated. Those people who had selected that candidate now select their next highest, and the votes are compared again. Last place is eliminated again. Eventually a winner emerges.
One way to approach this idea is through a school-like memorization of the algorithm. If there are other methods of voting, you memorize each one and can quickly recite each. But you end up retaining the information as an unintegrated set of facts, with no real understanding of the purpose, use, strengths, or relationship to other methods.
A common response at this point would be that it makes no sense to understand this in any kind of productive way. There's no chance that you will get to decide how the voting system should work, and trying to convince others to make a change is basically impossible for most people. This is a compelling argument and will dissuade most people from pursuing it further.
But even if that is true, it's not the final word. The way political change happens is when ideas spread. You don't have to singlehandedly change the world. But you can participate in the process. On top of that, a productive understanding of an idea unanticipated insights and clarity. Finally, the cost of productive understanding is not substantial. It can be easier than trying to rote memorize a subject.
So what does it mean to have a productive understanding? How does it relate to this voting method? One way to think of being productive is to be able to explain merits of the idea and compare it positively to existing voting systems. If you have a deep enough understanding to be able to explain it to others and to successfully deal with critiques, then you have a productive understanding of it. You could use that knowledge, not just to show what you know, but to persuade others.
So if you are seeking a productive understanding, you might start by asking what need this new voting system is attempting to satisfy. Why change what we have?
The current single vote system has a notorious problem that voters need to vote for a candidate that they think will win instead of one that they want to win. You might vote Democrat instead of Libertarian because you don't want the Republicans to win and you don't think the Libertarian candidate can beat them. People often end up voting for their second or third favorite candidate because they only have one chance. They have to try to anticipate where their vote will do the most good.
This means that people often are voting against a candidate, instead of for one. And those interested in third parties will feel that if they vote along those lines, their votes will be wasted. How many people would prefer a third party? It's difficult to say because they can't make their preferences known through voting.
IRV solves these issues by letting a person vote for the candidate they want, without ever wasting their votes. If the candidate that they prefer does not win, they essentially get to change their votes. Instead of people having to try to guess which candidate is "electable", or having to choose between voting for the candidate they want and the candidate they prefer over the others, IRV gives the best of all worlds.
Another problem with the existing system is that if people do decide to vote for a third party, it may give an advantage to the party they favor least. This is often called "splitting" votes. A third party might come in and split the fiscally conservative vote, for instance. IRV solves this.
In terms of productive understanding, recognizing the existing context is critical. You can know that the existing method leads to voters being afraid to vote for their favorite candidate, that it leads to minorities winning when the majority's votes are split, and that third parties are essentially unviable because not enough people are willing to gamble that they can beat the opposition. The need that IRV satisfies is for voters to pick the candidates they want without fear of these undesirable effects. It also avoids mistakes in the guessing of which candidates are viable and whether third parties can get enough of the votes. If the voters don't need to worry about any of that, they won't have the opportunity to make mistakes in their predictions. Voting can be based on preferences, instead of predictions of other people's preferences.
Understanding the need and the context are important. By seeing the purpose, the details of the mechanism can be more readily grasped and retained as a solution to these problems. You don't have to memorize the mechanism. By knowing the problem, most of the details become clear. You want a mechanism where people vote for the candidates they want, but if their candidate loses, lets them recast the vote between the remaining contenders. That means they can vote the way they want, and change it if it actually would have been a waste. The fact that this can be done through a ranking process and repeated "instant runoffs" is a useful method of implementation, but is just one possibility. Still, it helps to concretize the concept and to know one easy way it could be made to work.
Getting a productive understanding of this concept is more than just memorization of an idea. You can see that by grasping its need and relationship to the existing system, you may get a better understanding of how it works now. You can see how voters change their behavior to avoid existing problems, and how that can have wider effects like an inability of third parties to win or gain substantial support. All of these details come from trying to gain a productive understanding of IRV.
The general approach to productive understanding is to ask yourself how you should approach this topic if you needed to get results with it. The need to persuade others is one possible use. In areas that are more directly applicable to your life, you would ask how you can use these ideas to benefit you. If you are trying to understand life as the standard of morality, the goal would be to figure out how to understand it in a way that you can actually use it. How do I choose between these two options that both seem reasonable but lead to very different results? Can life as the standard help me?
A 'productive' use that isn't productive is winning a debate. You might win by drowning the other in details, or successfully promoting a logical fallacy, or confusing them, or overwhelming them, or just appearing to have a better idea. But all of this allows you to retain a very superficial understanding of the topic. A productive understanding requires enough depth that you can achieve results with it. Persuasion and winning a debate are two entirely different things. Persuasion requires you to be able to provide arguments with such merit that the other personal eagerly accept the idea. Winning a debate is easier and often won't lead to real persuasion.
The exact purpose you choose as a measure of productive understanding is not critical. The more productive the purpose, the more objective a standard it is for determining whether you have understood the topic correctly.
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