Explain something easy to me.
November 5, 2012 6:30 PM   Subscribe

Can someone explain the 512 paths infographic to me?

Something isn't clicking for me with this. The actual number of 'win' nodes displayed in the graphic for each candidate does not come anywhere near X in the 'Y has X ways to win' statement at the top of the graphic. I know I'm missing something elementary, but if someone could indulge my brain fog today I would be very grateful.
posted by ossian to Grab Bag (10 answers total) 2 users marked this as a favorite
The paths are laid out in order of electoral votes, which limits the paths you actually see at first. If you make out-of-order choices at the top, it will show different paths.
posted by zug at 6:32 PM on November 5, 2012

Best answer: Most of those paths are cut off. If Obama wins Florida and Ohio (going left from the root of the tree), it doesn't matter what happens in North Carolina, Virgina, Wisconsin, Colorado, Iowa, Nevada, or New Hampshire, even though there are 27 = 128 different ways for those states to divide their electoral votes. So Obama winning Florida and Ohio is really 128 ways to win, not 1.
posted by dfan at 6:41 PM on November 5, 2012 [2 favorites]

Response by poster: Thank you, dfan. Sanity restored.
posted by ossian at 6:49 PM on November 5, 2012

dfan's got where the "512" number comes from. However, there's another thing that should be explained about this infographic, which is that it's mostly nonsense:

Not all of those 512 possibilities are equally likely, so the observation that "Obama has 431 ways to win, which is 84% of paths" is not something from which you can draw the conclusion "Obama has an 84% chance to win". If each state were a fair coin, it would be meaningful. Each state is not a fair coin, though.

It is pretty neat to play with, though.
posted by Flunkie at 6:51 PM on November 5, 2012

However 84% is pretty close to the odds I'm seeing in a lot of places. Approximating every swing state as a fair coin isn't too bad.
posted by madcaptenor at 7:06 PM on November 5, 2012

It's true that 84% is close to the odds that many places have calculated, but I think that to a large degree that's coincidence.

For example, click on "Republican" for both Florida and North Carolina. The percentage of paths for Obama drops from 84% to 52%. In reality, both Florida and North Carolina are expected to go to Romney -- North Carolina pretty strongly expected to -- and they're not particularly important for Obama. According to 538, Florida has about a 1.3% chance of being the tipping point state, and North Carolina about a 0.3% chance. In contrast, Ohio 50%.

Another example: click on "Republican" for both Ohio and Nevada (also unclick for Florida and North Carolina). Obama now has over two out of three of the remaining paths. I seriously doubt you'll find anyone who would argue that Obama would have even anywhere near a two in three chance of winning even if he loses both Ohio and Nevada.
posted by Flunkie at 7:52 PM on November 5, 2012

Actually, now that I think about it, there's an even easier explanation why the 84% is mere coincidence:

In the past three weeks or so, Obama's chances of winning have been calculated to be, on various days, anywhere from 61.1% to 92.2%. That's a pretty big range. Meanwhile, the "percentage of paths" has always been 84%.
posted by Flunkie at 8:42 PM on November 5, 2012

Meanwhile, the "percentage of paths" has always been 84%.

Is that true? See Silver's list of competitive states from October 31. The definition is pretty liberal: he calls a state competitive if it's within ten points.

The nine states in play according to the Times graphic are WI, NV, IA, NH, OH, CO, VA, FL, NC (from most Democratic to most Republican). The states to the left of Wisconsin have 237 electoral votes all together, and the states to the right of North Carolina have 191.

Now say that momentum shifted towards Romney in such a way as to put Pennsylvania in play and take North Carolina out. Then Obama would have 217 EV to start with; Romney would have 206; and the middle 115 would be in play:

PA (20), WI (10), NV (6), IA (6), NH (4), OH (18), CO (9), VA (13), FL (29).

Here Obama needs 53 to win, 52 to tie. There are 298 wins and 9 ties possible, out of 512 possibilities; it's generally figured that Romney wins in an electoral tie, so let's give Obama odds of 298/512 = 58% here.

Similarly, say momentum shifted towards Obama in such a way that Wisconsin was out of play but Arizona moved into play. (I'm ignoring the damn Nebraska second district.) Then Obama starts with 247, Romney with 180, and the following states are in play:

NV (6), IA (6), NH (4), OH (18), CO (9), VA (13), FL (29), NC (15), AZ (11)

There are here 479 ways for Obama to get at least the 23 EV he needs, so we give Obama odds of 479/512 = 94%.

I'm not claiming this is exactly what would have happened with the percentage of paths method -- and certainly it suffers from the flaw that the answers move in discrete steps as states come into or out of play - but the answer it gives can change.
posted by madcaptenor at 9:28 PM on November 5, 2012

Sure, certainly if you consider different states, you'll get a different number. But I don't believe that over the entire course of the 61%-92% timeframe, they would have considered different states (assuming they would always consider the same number of states), and thus they would have gotten that same 84% number for every day in that range.

I may be wrong about that (I don't think I am, but maybe), but at the very least they certainly wouldn't have considered different states on October 31. Silver gave Obama a 79% chance on October 31, as opposed to 92% now, with the same states being the ones that would have been considered. That's a significant difference, especially over the span of less than a week.

In any case, if you don't like that argument, there's still the "just play around with it" argument. It considers Florida and North Carolina to be significantly more "must win" for Obama than it considers Ohio and Nevada to be, which is pretty unequivocally the opposite of reality - Obama can win pretty handily even while losing FL and NC, whereas if he loses OH and NV, he's likely toast.

The reason it takes this seriously wrong position is merely because FL plus NC have 44 votes, whereas OH plus NV only have 24; unfortunately, that's not a good reason to take that position.
posted by Flunkie at 10:26 PM on November 5, 2012

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