Many people move chaotically from thought to thought without explicit structure. Inappropriate structuring may leave blind spots or cause the gears of thought to grind to a halt, but the advantages of appropriate structuring are immense:

Correct thought structuring ensures that you examine all relevant facets of an issue, idea, or fact.

• It ensures you know what to do next at every stage and are not frustrated or crippled by akrasia between moments of choice; the next action is always obvious.
• It minimizes the overhead of task switching: you are in control and do not dither between possibilities.
• It may be used in a social context so that potentially challenging issues and thoughts may be brought up in a non-threatening manner (let's look at the positive aspects, now let's focus purely on the negative...).

To illustrate thought structuring, I use the example of Edward de Bono's "six thinking hats" mnemonic.  With Edward de Bono's "six thinking hats" method you metaphorically put on various colored "hats" (perspectives) and switch "hats" depending on the task. I will use the somewhat controversial issue of cryonics as my running example.¹

Followup to: How Much Thought

A trolley is hurtling towards three people. It will kill them, unless you pull a lever that diverts it onto a different track. However, if you do this, it will hit a small child and kill her. Do you pull the lever, and kill a child, or do nothing, and let three adults die? This question is used to test moral systems and theories; an answer reveals how you value lives and culpability. Or at least, it's supposed to. It's hard to get a straight answer, because everyone wants to take a third option. Why waste time thinking about whose life is more valuable, when you could be looking for a way to save everyone?

In philosophy, decisions are hardened by saying that there are no other options. The real world doesn't work that way. Every decision has an implied extra option: don't decide. Instead, put it off, gather more information, ask a friend, or think more. You might come up with new information that affects the decision or a new option that's better than the old ones. It could be that there is nothing to find, but it takes a lot of thought and investigation to be sure. Or you could find the perfect solution, if only you wait a few more seconds before deciding.

We can't think about both a decision and a meta-decision at the same time, so we have a set of readiness heuristics to tell us whether we're ready to call our current-best option a final decision. Normal heuristics determine what we decide; if they go awry, we choose poorly. The readiness heuristics determine when and whether we decide. If they go awry, we choose hastily or not at all. Broken readiness heuristics cause decision paralysis, writer's block, and procrastination.

As Robin Hanson is fond of pointing out, people would often get better answers by taking other people's answers more into account.  See Aumann's Agreement Theorem.

The application is obvious if you're computing an answer for your personal use.  But how do you apply it when voting?

Political debates are tug-of-wars.  Say a bill is being voted on to introduce a 7-day waiting period for handguns.  You might think that you should vote on the merits of a 7-day waiting period.  This isn't what we usually do.  Instead, we've chosen our side on the larger issue (gun control: for or against) ahead of time; and we vote whichever way is pulling in our direction.

To use the tug-of-war analogy:  There's a knot tied in the middle of the rope, and you have some line in the sand where you believe the knot should end up.  But you don't stop pulling when the knot reaches that point; you keep pulling, because the other team is still pulling.  So, if you're anti-gun-control, you vote against the 7-day waiting period, even if you think it would be a good idea; because passing it would move the knot back towards the other side of your line.

Tug-of-war voting makes intuitive sense if you believe that an irrational extremist is usually more politically effective than a reasonable person is.  (It sounds plausible to me.)  If you've watched a debate long enough to see that the "knot" does a bit of a random walk around some equilibrium that's on the other side of your line, it can make sense to vote this way.

How do you apply Aumann's theorem to tug-of-war voting?

I think the answer is that you try to identify which side has more idiots, and vote on the other side.