Thia is an experimental attempt to measure the counterfactual. Instead of conditional N/As, conditional options, scaled (dice roll) zoom ins, or some such, this market has what I call "inverting" resolutions.
You're welcome to add more options, too!
Resolution
If Trump wins, business as usual
everything TRUE resolves YES
everything FALSE resolves NO
If Trump doesn't win, it's inverted
TRUE -> NO
FALSE -> YES
Nitpicks:
Anything unknown when Trump wins/ doesn't win will be given a week for proof to surface, and otherwise will resolve as FALSE.
If Trump drops out early for any reason, this resolves to the state of the world at that point via the "doesn't win" lens.
How to read this market
"If X happens, will Trump win the election?"
If an option at high value happens he's more likely to win. That is to say it's "correlated" to his chances.
And the reverse is also true. If an option at low value happens he's less likely to win. It's "anti-correlated."
Moreover, you can infer the effects of options that don't happen.
The further away the value is from Trump's odds indicates a combination of how dramatic the effect would be + how likely it is to happen.
How to bet on this market
I'll get into the math, but the basic question is, "How might this affect his chances of winning?" If it improves it, the simple answer is to bet YES, if it hurts it, the simple answer is to bet NO.
The current math for optimal betting:
T= Your odds that Trump wins, 0 to 100%E= Your odds that the option's "Event" happens, 0 to 100%R= How correlated you think they are, -100 to 100% (from severely hurts him to majorly helps him)(Treat all as decimal)
Your target odds =
(TE+(1-E)(1-T))(ER+1)Aren't sure how strong the effect would be? It's also totally valid to use a range of
R! Try two values between -0.5 and 0.5, then make sure to bet the market so it stays in that box
For example, if your credence of a Trump win is 55% and China invading Taiwan is 10%, but you think it would only help or hurt him a little bit and aren't sure which way (±25% correlation), your range to keep the market between is 45-47%. If you think invasion means he's guaranteed to lose the election (-100% correlation), then your target at those odds is 41%.
But where this gets interesting is as the odds of such an event go up. If it's suddenly 90% likely and would tank his chances, your target becomes 5%!
For reference:
Related questions
hmm I've noticed an issue with my own recommended math. If E is solved (0 or 1), then intuitively your target price should be (1-T) or T, respectively, right? (assuming that now the correlation effect is priced in, so R = 0)
in that case, this formula breaks down. maybe it's because of the assumption that R = 0? or maybe I'm way off on what your target odds should be when E is solved.
for now, it's good enough, but I want to do right by you all so I'm in the process of scratching out a new one. hopefully I can figure it out!
okay, I've found a formula that is much more accurate. it's more complicated (*sigh* of course it is), but I think it's better. I'll post the full write up and details later tonight or tomorrow. in the meantime I havent been trading since I realized and wont resume or edit limits until after I've posted it. I was also proven wrong on an assumption or two. A couple things to know:
events with low odds naturally have a smaller effect on his chances no matter how influential they'd be (oops)
nothing has changed about the resolution or the basic principles of the market!
new math is up! the formula:
(TE+(1-E)(1-T))(ER+1)
This results in a few things, most of which are intuitive:
If the chance of the event happening (E) is 1 or 0 (guaranteed resolution), then the target percent to bet to becomes T (Trump's odds) or 1-T respectively, if in that case we assume it is priced in so correlation (R) = 0
Likewise, when T is 1 or 0, but somehow this doesn't resolve yet, the target percent is E or 1-E, if R=0
Stronger correlation R means stronger effect
Same for stronger anti-correlation
Higher likelihood E means greater range of target percents based on R
Low likelihood events (<50%) seem to anchor opposite Trump's current odds (1-T), and the lower they are the more significant this effect is
It took me awhile to get to this, and I had made some bad assumptions originally.
I thought that all the prices should be swinging around Trump's current odds, but clearly there's a natural second focal point at the inverse, 1-T. I knew that when either E or T was solved, R should equal 0 (in other words, already be priced in to Trump's chances), and the prices should converge on the focal point(s). The old formula didn't do this and instead went completely off the rails at the extremes, which is how I realized it wasn't quite right. Would it have given us confidence in bad bets? Mostly it was okay (until it wasn't) but certainly those bets wouldn't have been mathematically optimal.
As an aside, I don't recommend trying to write a formula from scratch when all you know is "when E is 1, the result must be T; when E is 0, the result must be 1-T; and somehow R needs to be crammed in there." But if those assumptions are correct then now we can trade with more confidence.
I'll probably only run the math occasionally myself. No way I want to plug everything in every time! Just gotta calibrate my instincts and then betting should be a breeze.
What I find most interesting is as this market stabilizes, you feasibly could work backwards to calculate how far Trump's odds should move as events happen!
I've significantly rewritten the description to better explain how this market works. Big thanks to @HarrisonDorn for nerd-sniping me into formulating a mathematical model that is hopefully correct.
Is this better? Let me know if there are more questions!
edit: I'm probably wrong read Pat's comment
In English:
("You've woken up Nov 5, 2024, and you found out that Trump has won, what do you think is the chance X has already happened?") x (chance of Trump winning)
+
("You've woken up and found out that Trump has not won the election, what do you think the chance is that X hasn't happened?") x (1-chance of Trump winning)
= YES position chance
This is a really cool market!
hmm I don't think this math is quite right, though! look at the example Biden drops out 50% & Trump wins 80%:
if,
(0.5 x 0.8) [drops out, trump wins] + (0.5 x 0.2) [doesn't drop out, trump loses] = 100% YES
(0.5 x 0.2) [drops out, trump loses] + (0.5 x 0.8) [doesn't drop out, trump wins] = also bet to 100% for NO!
But we know that the following cases should resolve NO:
Biden doesn't drop out, Trump wins
Biden drops out, Trump loses
So the bottom of your range (where, at minimum to bet YES to) can't be 100%.
Here's the math I used for the examples:
T = Trump wins
E = Event happens
Target for NO, hurts his chances = T - (0.5 - E)
Target for YES, helps his chances = T + (0.5 - E)
Giving a target range of:
Biden drops out 50%, Trump wins 80% = 80 to 80%
China invades Taiwan 10%, Trump wins 80% = 40 to 120% (capped to 100)
The question then becomes one of correlation. You should be betting at least towards your range if the value is outside it (accounting for interest rate and edge), and then directionally within your range by how you think it'll affect his chances.
In reality this means to find your real target value there's another hidden value for Correlation ("R"), which is from -1 (perfectly anti-correlated, hurts his chances) to 1 (perfectly correlated, helps his chances) with 0 being completely uncorrelated:
Target = T + (0.5 - E) * R
Which for "China invades Taiwan 10%, Trump wins 80%" results in:
if China invading means he loses the election, 0.8 + (0.5 - 0.1) * -1 = 40%
if China invading somewhat helps him (R = 0.25, aka helps him by 25%), 0.8 + (0.5 - 0.1) * 0.25 = 90%
The silly part is when something anti-correlated has a high chance of happening. Say you disagree with the going market rates and think China will almost certainly invade (E = 0.9) and that it will severely tank his chances (R = -0.75), but for some reason think that he's still got that 80% chance of winning:
Target = 0.8 + (0.5 - 0.9) * -0.75 = 90%
In that weird scenario, you want to bet to 90% due to the inverting resolutions! In reality, if your credence for events happening or Trump winning are way different than going market rates, any strongly anti-correlated factor with a high chance should significantly reduce your credence of T.
And if my model is correct, then the following is true:
if one of these events has a 50% chance of happening, then its correlation has no effect and its spot in this market should be arbed to Trump's chances of winning
if one of these events is completely uncorrelated to Trump's chances of winning, it should also be arbed to his chances
But I think most of these have at least some small correlation or anti-correlation, otherwise I wouldn't have asked the question!
This has gotten decent traction! @Nikos pushed the market to Basic with a lovely subsidy of 10k ❤
I'll likely push it just a bit more up to Plus soon, so if there are more options you want to see, add them while it's still cheap or let me know what they are so I can add them
I've created and added the tag "Advanced Market Format" for this & other complicated market structures that aren't for the faint of heart. I'm sure I haven't been the only one to do this particular structure, but I'm probably the first to acknowledge the math and weird ways it can work. I'm excited to see if it pans out!
Still hoping to get more advice on how to explain it simply and effectively.
The point:
an experimental attempt to measure the counterfactual
And if you're intimidated, then don't bet! I agree it's complicated. But hey, some of us like trying to measure difficult-to-measure things
@ChrisMillsc5f7 I did some redrafting of the description with someone who doesn't use Manifold. it's still a complicated market! but hopefully coherent now