Sunday, 13 June 2010

Day 164, on which John with the whole 'choiceline' thing [13.6.10]

Dag hundrede fireogtres. I hate revision. I really, really hate it. With a passion. Or an anti-passion, to be more exact. I spent the whole day at my computer, typing up notes from a year's worth of geography lessons. God damn you, AQA. Actually, I lied a teensy bit there; I didn't spend the whole day revising. Those nice people at Steam held a weekend of playing Team Fortress 2 free as a result of it being released on Mac. I downloaded it yesterday and got to play it today. At the start, I wasn't very impressed as a) I kept dying and b) I kept missing when trying to shoot other people. However, once you learn to utilise the different classes, it's a load of fun.

OK, back onto our choice graphs. Read yesterday's post before you start on this one, because I'm building on the stuff from that post, and it's starting to get more complicated.

So, let's return to Ben, who's buying a drink from a shop. He's got four outcomes and one quanitified group of outcomes ('none'). Now we're going to expand on the second choiceline diagram (last one of last post):

Here you can see we've created a second event. Remember that with these choice graphs, we only show what we want to see, because there's an infinite number of outcomes for any event. All we're doing is displaying the bits we want to see, to compare them to each other. That's why we've only continued one outcome on the diagram above.

Note that:

  • The other outcomes from the primary event (first event) have not been extended, even without secondary events. If we stretched the 'Coke' outcome to be at the same height of the secondary outcome line, then we are dismissing secondary events of that outcome. Considering the options we have, there would be a '! Way of asking' secondary event on the 'Coke' outcome too, and we can't ignore that. You can ignore different outcomes, but you can't ignore whole events, as they affect the probability of the choiceline you're following.
  • We've stretched the 'None' outcome from the primary event further to the right, to compensate for the extension of the 'Beer' outcome's space. Remember that probability is cumulative. That is, Ben's chosen Beer, and that's quite improbable. So, anything he does next would not be more probable, because he's already made an improbable decision and that's affected the probability of what he could do next.
  • As with before, none of the outcomes are the same probability as the event which leads them, because probability is cumulative and if they ran in a straight line, they'd be ignoring the probability of events that have happened before.
  • Just like the y-axis, the x-axis (Probability) has no scale; it simply shows outcomes' probabilities in relation to each other. By this I mean that it shows that if outcome a is to the left of outcome b, then a is more probable than b, and there's no measure of how more probable it is.
  • There's always arrows on the ends of the outcomes to show that time goes on, and that this isn't a definite timeline (it's an infinite timeline; it could go on forever).
That's enough for today, because I'm tired with revision. I have a couple more diagrams to go (including, when we get to it, one with two different choicelines interacting), and then we'll be off this complicated topic, and onto other philosophical things.


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