# 179

(Disclaimers: I work in the financial industry, though not in a way related to prediction markets. Anything I write here is my opinion and not that of my employer.
This is a US-centric piece based on a case study of PredictIt: as some people have pointed out in the comments below, if you are outside the US you may have substantially better options.)

## SECTION I: INTRODUCTION

So there's an argument that I've seen a lot over the past few years, particularly in LW-adjacent circles, that goes something like this:

You say you believe X is likely to happen. But prediction markets say X is likely not to happen. Since markets are efficient, you must be wrong. Or if you do know better than the market, why aren't you rich? Since you haven't bet on that market to make free money, you must be lying. Or stupid. Or both!

This post is dedicated to disagreeing with that argument, not from an anti-Efficient-Market Hypothesis position, but from a pro-Efficient-Market Hypothesis position. My position is:

The argument above is pretty much sound if we are discussing mainstream financial markets. If someone claims to have better information than a mainstream financial market on the value of Google stock, or of copper, they ought to either use this knowledge to make a huge amount of money or stop talking about it. However, it is not true if we are discussing prediction markets. Current prediction markets are so bad in so many different ways that it simply is not surprising for people to know better than them, and it often is not possible for people to make money from knowing better.

I've been meaning to write this for a while, but got tipped over the edge by the recent post here, which talks about the limitation of prediction markets being the correlation of the events they predict to other assets, and their consequent value as hedging instruments. That is...well...it's not wrong exactly, but there are so many other problems that are so much bigger that I felt it was worth laying (some of) them out.

Math follows. I will be focusing on PredictIt for this analysis. Other prediction markets may work a bit differently, but similar analysis is applicable to any of them. If you think the math is wrong I am happy to discuss/make changes, but I very much doubt any changes will materially alter the final message.

As of this writing PredictIt has Donald Trump at 40% to win the election (or, to put it another way, you can pay 40 cents for a share that pays out $1 if Trump wins). Suppose you think he is more/less likely to win. How likely/unlikely does it need to be for Trump to win for you to make money (in expectation)? Or, to put it another way, what range of probabilities for Trump to win are consistent with the prediction market values? ## SECTION II: REASONABLY SIMPLE PROBLEMS 1: Spread. This is only a small problem, but it is non-zero. PredictIt will sell me 'Donald Trump wins' shares for 40 cents, but will sell me 'Donald Trump loses' shares for 61 cents (which, from a finance perspective, works out very similarly to letting me sell 'Donald Trump wins' shares for 39 cents). So if I think there is a 39.5% chance of Trump winning, there is no way for me to make money off of it: I can buy 'Trump wins' shares for 40 cents, or sell them for 39 cents, and if the true value is 39.5 cents both of these will lose me money. The range of possible probabilities for which you cannot make money starts at 39-40%. 2: Transaction Fees. PredictIt charges a 10% fee on profits (see https://www.predictit.org/support/how-to-trade-on-predictit). As far as I can tell, it does not net profits against losses before calculating these fees. That is to say, if I make two$100 bets at even odds, win one, and lose the other, PredictIt will charge me a $10 fee on my winnings on the bet I won, even though overall I have made no money. So if I think there is a 50% chance of Trump winning, and spend$100 buying Trump Wins shares, instead of my expected final money being 50% * $250 =$125 for a $25 profit, my expected final money is 50% * ($250 - $15 ) =$117.5 for a $17.50 profit. After accounting for this, the range of possible probabilities for which you cannot make money is: 3: Withdrawal Fees. When I actually attempt to withdraw my money from PredictIt, PredictIt charges an additional 5% fee on the withdrawal, giving me only 95% of my money back. How important this fee is to any given bet varies depending on how many bets I make on PredictIt (if I am making multiple bets without withdrawing money the effective impact of the fee on any given bet is smaller), but for now let's assume that (like most people) I do not have a PredictIt account and would need to create one to make this bet, and then withdraw my winnings immediately afterwards. If so, my effective winnings shrink again as 5% of my money (not just my winnings, all the money I deposited) disappears to PredictIt. After accounting for this, the range of possible probabilities for which you cannot make money is 4: Investment Interest Rate/Time Value of Money. The presidential election will not happen until November. Let us be generous and assume that PredictIt settles bets immediately thereafter (though their page for the bet states 'PredictIt may determine how and when to settle the market based on all information available to PredictIt at the relevant time' and 'PredictIt’s decisions and determinations under this rule shall be at PredictIt’s sole discretion and shall be final'). It is currently July. That means it will be ~4 months until the bet resolves, during which time your money will be tied up in PredictIt. What else could you be doing with that money? Well, depending on who you are, you could be getting reasonably risk-free returns via e.g. Treasuries or bank accounts, but those interest rates are low. On the other hand, your bet is de facto a loan to PredictIt as well as whatever bet you think you made. If PredictIt suddenly goes bankrupt in a massive downturn, or if whoever runs it takes the money and flees to Dubai, you may not get paid back. So, what effective interest rate would you charge to loan PredictIt money in the current financial environment? How risky an investment is it? If you would charge it 5% per year (which I don't think is all that high by the standards of bonds in risky companies), then over those 4 months you could have made about 2% return without the prediction market involved. (Side note: this effect is larger or smaller depending on what event you are considering and how far in the future it lies. There's some reason to expect that this will make prediction markets a little more efficient as the event they pertain to draws closer, but there are still quite a few other problems). After accounting for this, the range of possible probabilities for which you cannot make money is: So at this point, the 40% probability we see for Trump to win on PredictIt is completely compatible with any probability from 31.8%-45.7%. This is already...rather a wide range. And this is before we encounter two rather larger issues: ## SECTION III: HORRIBLE MESSY PROBLEMS 5: Taxes Note: I am not a lawyer! I am particularly not a tax lawyer! This section is speculative, even more US-centric than the rest of this piece, may well be wrong, and even if it is right your tax situation may be different! As far as I can tell, PredictIt winnings are treated by the US government as income. This means two things: first, that if you win money on PredictIt the US government will tax it; and second, that if you lose money on PredictIt the US government will not let you net it against anything. So, just like PredictIt's fees did, taxes require you to have a much higher chance of winning in order to be net-positive. If you have a good accountant and think you can net PredictIt losses against another tax bill, or avoid paying taxes on PredictIt winnings, this might not be applicable to you. If we assume you pay a 15% tax rate (according to Google this is pretty close to the nationwide average), the range of possible probabilities for which you cannot make money is: And if we assume you are paying 35% income tax (which requires a high salary, but I suspect a lot of the people who we're hoping will come and correct the prediction market for us have high salaries...) then the range of possible probabilities is: So now we're fully compatible with Trump being anywhere from below a one-in-four to above a one-in-two chance! And then we encounter the really big one. 6: Betting Limits Part of how markets work is that people who know better will eventually be able to command more of the money. If I am able to predict the price of Apple stock better than anyone else, I can multiply my money faster, I can use my track record to get other people to invest with me, and I can direct large quantities of money, which both makes me a lot of money and allows me to move the market to a more accurate valuation. PredictIt places a limit of$800 on your position in any one bet.

At the market level, this means that you can no longer rely on small numbers of intelligent people to fix market prices for you. Since a small number of intelligent people can only mobilize at most $800 each, you are reliant on lots of different people intelligently picking the right price. And at the individual level, this makes it difficult to make any amount of money that matters off a prediction market. In a real financial market, people will invest large amounts of money. If a hedge fund pays ten million dollars a year hiring dozens of smart people to discover a way of making 1% excess return, so long as they are investing at least a billion dollars that is worth it. Therefore, in a real financial market, there is reason to expect that any analysis that can correct market prices will be done, even if it is difficult and expensive to do. PredictIt can just about manage to let people who can correct market prices make enough money to merit creating an account there. Recall that, even with zero taxes, the range of possible probabilities for which you could not make money was: But this is the range of probabilities for which you cannot make any money at all. Suppose that you think Trump's chance to win is 50%. If you invest the maximum$800, you will end up with in expectation:

which gives an expected profit of about $75, and that was without considering taxes. If you face a 35% tax rate, and think Trump's chance to win is literally zero, after investing$800 you end up with:

making a profit of about $250 in exchange for knowing with absolute certainty that an event a prediction market has at a 40% probability is guaranteed not to happen. This is not sufficient to merit dedicating time and effort to research. ## SECTION IV: CONCLUSION If someone claims that they are absolutely certain Trump will/will not win the election, they should be able to make money on a prediction market from this prediction. However, they may not be able to make very much money at all, and even if they are quite confident that the prediction market is wrong it may not be worth their time. Assuming that this person should be willing to bet on their views on a prediction market may be merited, but even from a purely financial view it is a much closer affair than you may think. If someone claims that Nate Silver and 538's analysis team know better than a prediction market what Trump's odds of winning the election are, they are quite likely correct. It is not possible with prediction markets in their current state for them to make money from that knowledge. If you dismiss this person because they haven't bet on prediction markets, you are actively wrong, you are making me and a system I believe is a good idea look bad by association, and I would like you to stop talking about this. # 179 48 comments, sorted by Highlighting new comments since New Comment I feel this is more "limits of PredictIt" rather than "limits of prediction markets". Doing the equivalent analysis for Betfair for someone in the UK. (2% charge on profits, no fee for withdrawing). Right now the market for Trump to win is (£1200) 2.78 / 2.80 (£7421) Those imply probabilities of 35.97% and 35.71% After fees, 36.44% and 35.00%. That's not a bad spread, and you can do this in much more size. (If you're willing to work a bit, you can comfortably get on £10,000s at prevailing levels). We pay no taxes on gambling, so there's none of Section III to worry about. (Admittedly, once we start talking about even more serious size we run into Betfair's Premium Charge, but for your average UK based rationalist, I don't think Betfair is as bad a prediction market as you're making out). It's possible! I'm writing this from a very US-based perspective, where the main prediction markets I hear talked about are PredictIt and IEM (and I think IEM might be even worse for betting at scale?) If you have access to a prediction market where these problems are smaller/nonexistent, it will be more accurate. And 2% charge of profits is much lower, plus looking quickly at the Betfair website it seems to have a pretty good amount of liquidity at a reasonably small spread. I'm not sure how accessible Betfair is to someone from the US from a legal/tax standpoint, so the overall point may still stand if you're talking to someone in the US/if you think that a lot of the people informed on a given issue are in the US. (And do you really have zero taxes on gambling profits? I would not have guessed that). Why don't you consider this a bigger objection to your post? IMO it's actually very important that a deep, liquid prediction market with millions of pounds of volume and low fees exists, and the prices are fairly similar to PredictIt. IMO this is strong evidence that, in this case, PI's prices aren't being distorted too much by the problems you list. I believe US-based bettors can get >1m USD on Trump or Biden at fairly close to Betfair odds with a little bit of time and patience as well through various means; I am aware of several people that have bet >$100k on the election and I think they could bet substantially more if they want to. (some examples of "various means": crypto exchanges, finding e.g. poker players who want to bet a lot on the election, finding a friend in the UK to bet on betfair for you)

Two replies here, I think:

First, are any of the things you suggest in fact legal for US-based bettors?

Second, how difficult in terms of time/inconvenience/up-front capital costs without the potential for leverage are they compared to the ways in which you can bet on e.g. the price of Google stock?

If you're telling someone in the US "you should be willing to bet your views on prediction markets, if you're right it's free money" when what you mean is "it's free money provided you're willing to dedicate hours to working your money through crypto exchanges, committing tax fraud along the way", that feels somewhat different.

I would be willing to tell someone who thinks Google shares are underpriced "go buy some then," because buying Google stock at low cost is legal, very easy, and even if you have limited up-front cash the real financial markets offer opportunities for leverage (options etc.)

I would not be willing to tell someone who thinks Trump Wins shares are underpriced "go buy some then" when that process is time-consuming, difficult, and likely illegal.

Yes, it's completely legal for people in the US to bet on things; the only illegal part is being an intermediary.

I see where you're coming from re "you should be willing to bet your views"; I just want to be clear that if you think PI prices are inefficient, it's mostly not because of transaction fees/taxes/etc.

How about telling someone who thinks Trump Wins shares are underpriced "go search on twitter and poker forums for people betting on this, and message a few of them"? This is completely legal, doesn't take that long, and is quite safe as long as you both agree to trustworthy escrow. There's no guarantee you'll find anyone willing to take your bet, but I think the chances you would are fairly high.

1. I don't agree that the prices are fairly similar. PredictIt, poly.market, Omen, and FTX (let me know any other crypto exchanges you want considered) all have Trump ~40%. Betfair has him ~35%. I think that's materially different. (Also, the volumes on those exchanges are all pretty limited, so I'd be impressed if you could get $1mm down that way). I agree you could potentially get some risk down via P2P betting, but I don't think it's fair to describe that as a "prediction market". (Although it does nuke his point of excusing people from not putting their money where their mouth is). 2. I don't think you can get$1mm of risk down on Betfair. (Because of the Premium Charge issue I mentioned). I think the only way I can see that being done at the moment is P2P, and I'm not sure I'd be comfortable with the counterparty risk involved.

According to Betfair you need to bet in over 250 markets to trigger the premium charge, and "Any single win that constitutes more than 50% of your gross profits over the lifetime of your account will be excluded from the calculation". I think the hypothetical person trying to bet $1m on the presidential race is safe. Regarding crypto, isn't Augur v2 theoretically supposed to launch soon? Fair enough, for a one off it might work, although that wouldn't be the case for someone who is regularly active in prediction markets. Theoretically on the 28th, but that doesn't answer my question about where you can currently get serious money down down in crypto? I don't know much about crypto, but I thought FTX was fairly liquid? I guess using it is a legal grey area for US citizens though. From looking at the orderbook it looks like you could get ~500k down over time without moving the price by more than 5c. (I guess it depends on your definition of acceptable slippage; to me 5c is fine) You were the one making the claims about crypto. FTX isn't accessible to US or UK based bettors for the Trump election. (So not a grey area, just not an area you can use at all). (I also refused to believe that liquidity is real. Whenever I see orders like that in an order book I am usually fairly confident that there is something subtle going on which means they have a technological way to avoid being filled. Looking into FTX, the subtlty is that you can't submit orders 2% thru' the order book, which means you can safely leave gigantic orders off-market to maintain queue spot or for other technical reasons). I know people living in the US have been able ot bet on FTX despite their ToS banning US citizens; I haven't done this so I don't know the process. Maybe it's straight up illegal rather than a legal grey area! (I think you might need to supply fake KYC docs which does sound kind of illegal now that I think about it?) Yeah, the US has a bizarre tax system, and seriously puritan laws about gambling (including treating most non-regulated investment return as gambling). If one were serious about this topic, the obvious answer is to move someplace more reasonable (and then wait 10 years for the US to stop expecting you to pay taxes on non-US activities). At the very least, the goodness of prediction markets in general should be studied outside the US, and a US-centric post would be labeled as "limits of betting markets in the US". I don't think that "lots of the informed people" being elsewhere should make much difference. The main metric for how seriously to consider data from prediction markets (in my mind) is open interest (or volume / liquidity if open interest isn't available). Yes - well, there are taxes on gambling profits, but on the betting companies, but not the individual gamblers. This is a great post! As a costly signal of me liking it, I went in and fixed a bunch of formatting mistakes and converted your equations to nicely centered LaTeX blocks. Do let me know if you prefer your version, and I am happy to revert it. Ah, someone with the time and energy to proofread and LaTeX things for me! No objection, thank you very much! (I actually didn't know other people were able to edit my posts though, how does that work?) I am an admin on the site, so I can edit things (other users can't). It's always been pretty common practice on LessWrong for mods/admins to clean up broken formatting, and it helps me feel the pain of the ways in which the editor that I build causes problems, so I feel more motivated to fix them. In around half of the equations there is an extra right parenthesis. It makes reading the equations a bit extra work as it changes the interpretations somewhat. In most of the equations with an extra right parenthesis, I believe it is the leftmost one (of the right parentheses) that should be removed. Oops, sorry, that is likely my fault. Will fix. (Edit: And I have now fixed it) First of all, I love this post, thanks for writing it. That said, you have not at all made a case for this part: If someone claims that Nate Silver and 538's analysis team know better than a prediction market what Trump's odds of winning the election are, they are quite likely correct. To make this case, it's not sufficient to argue that the betting market's implied probabilities are unreliable. We also have to argue that Silver & co are more reliable than the market. Personally, I'm still very skeptical of that - placing money on a prediction is a useful debiasing tool even if the bet doesn't pay for the analysis effort. Silver & co, on the other hand, at this point face basically the same incentives as any other journalists - not exactly a recipe for debiasing! They're going to get very-frequent positive feedback whenever their articles get clicks, versus only a single burst of feedback every four years on the accuracy of their models. Fair enough, that part is worded more strongly than I can really justify. I'd definitely still say it's quite possible that they are correct, and I still wouldn't think you can easily show them to be wrong by EMH-style reasoning. I think one way of putting this is, given that a successful prediction on PredictIt only pays for a few hours of work and the 538 team presumably has at least some full-time people, the 538 team has probably spent more money investigating these questions than the entire PredictIt market combined. (However, the incentives are different - a PredictIt player has an incentive to be right but 538's incentive is to tell a story that people who like reading about political statistics will find plausible and interesting) I think one way of putting this is, given that a successful prediction on PredictIt only pays for a few hours of work This is extremely far off! I believe on the order of 10-100 people on PredictIt make over$100k/yr, and if you're already interested in politics sitting around betting is a much easier & enjoyable way to spend an hour than most similarly paid work. (for reference I've made around $30k in the last 5 months while ostensibly being a full time student) Can you clarify how this is possible when the article claims you can only make$100-200 per bet even if you have perfect certainty? Do you just make tons of max value bets? I'm not sure how this site works except for what's described in the article.

• a lot of the costs in the article are on net profits rather than gross profits (eg. taxes, withdrawal fees, risk of PI going under). I didn't include taxes or withdrawal fees in that figure, but it doesn't change the order of magnitude (and ofc it's not clear yet what average tax rate I'll pay this year)
• you can make far more on a contract by trading on swings in addition to waiting for the final outcome (e.g. buy "Yes" at 20c, sell at 80c, then buy "No" at 20c and sell it at 80c).
• There's a large number of contracts to trade on for a single important event (e.g. to bet on Trump winning, you can bet $850 that Trump will win the presidency,$850 that a Republican will win the presidency, $850 that a Democrat will not win the presidency,$850 that Biden will not win the presidency, $850 that the next VP will be a man, and so on). They're usually not identical, but correlated strongly enough that you can get a lot of exposure to the event. There's also bracketed markets on e.g. the margin of victory in an election, where each bracket (e.g. Dems win by 0-1%) is a separate contract. A single MoV market might have 10 contracts, so you can bet thousands on it (and they tend to be volatile, so you can easily have 5 figure total turnover). Overall, PI seems to be a bizzare violation of EMH where you can extract large amounts of money for relatively little time/low skill To reasonably conclude that PredictIt's limits are "limits of prediction markets"—as your title asserts—you need to show either that the other existing prediction markets also exhibit these limits, or that there is a fundamental theoretical reason for expecting such limits to be exhibited by any prediction market. As far as I can tell, you do neither. (You do say that «similar analysis is applicable to any [prediction market]», but you never justify this assertion. In fact, of the six problems you note, I think the only one that may be plausibly claimed to be inherent to prediction markets is #4, and even that one may be potentially solvable.) Agreed - 4/ is solved by allowing margin. (Although margin is trickier if the event can suddenly resolve to 0 or 1 at any time, I think there are even solutions to this) A few comments from someone who regularly trades on PredictIt: 1) The maximum allowed bet is$850 (not $800), and this is only on a per contract basis. Therefore, if you are betting on Biden winning, you can max NO on Trump and YES on Biden for a total of$1700 in the same market.

2) PredictIt also has numerous overlapping markets which are all tied to the results of the general election. Currently all the markets below let you bet on the outcome in November, allowing your max bet in practice to substantially exceed the $850 limit. https://www.predictit.org/markets/detail/3698/ https://www.predictit.org/markets/detail/5960/ https://www.predictit.org/markets/detail/5961/ ...and this doesn't even include state specific markets or markets dealing with popular and electoral vote margins. 3) Many of the most successful players on PredictIt are excellent at playing the swings. Simply reacting to news quickly can net you hundreds (or thousands) in minutes, so there is often no need to hold for long periods of time. Conclusion: It is certainly possible for people to know better and also make a substantial profit on PredictIt. The$850 limit does impose a limit on profits for a single bet in a single market, but the wide selection of markets on the website allow a dedicated individual to research and react their way to a profitable edge in virtually every market, yielding good returns despite the fees. There is a very good reason the website has a dedicated user base.

"As far as I can tell, it does not net profits against losses before calculating these fees."

I can confirm this is the case based on the time I lost money on an arbitrage because I assumed the fees were on net profits.

A parallel problem with prediction markets: at non-financial-industry scales: they're used as signals of confidence. How often do you see, after someone makes a bold claim, a response saying to "put your money where your mouth is." But just the act of signalling confidence can be intrinsically valuable to the person making a claim. In bet-capped places like predictit, this can make equilibrium that are different from optimal, because there are non-monetary incentives at work.

Hey, I am interested in curating this post, but do think it would be good for the title to be more accurately scoped to be talking about PredictIt than all prediction markets. Something like:

"How wide is the spread on popular prediction markets? (PredictIt case study)"

Or

"Limits of Prediction Markets (PredictIt case study)"

would make me a bunch more comfortable with curating it. Do you think that's an option?

Sure, happy to change it. Does 'Limits of current US Prediction Markets' plus some commentary at the top to the effect of 'this is based on a case study of PredictIt, per some comments if you are outside the US you may have better options' sound reasonable?

Yep, that sounds totally sufficient.

EDIT: NVM. This is just proof I didn't get enough neonatal iodine.

For Section 2 on transaction costs you write the calculation for probability of winning is:

 100 / ( ( ( 100 / 0.40 ) * 0.9 ) + 10 )
Where does the extra +10 come from?

EDIT: It's so that you're not paying taxes on the amount of the original wager.

maximum_%_bet_on_P = bet_amount / (conditional_winnings - fees )

= bet_amount / (conditional_winnings(1-fee%) + bet_amount*fee%))

The +10 is because the 10% fee does not apply to your original $100, only to profits. So if you would have$250 without the fee, rather than 250 * 0.9 = $225, you end up with$235.

One thing I don't see mentioned here is PredictIt's advertising approach can bias markets. I haven't done much research into this myself, but a top PredictIt trader mentions in this post that PredictIt advertised on Breitbart during the 2016 election, bringing in lots of money from die-hard Trump supporters: https://politicalpredictionmarkets.com/blog/

Counter-argument: Other prediction markets (that presumably are not mimicking PredictIt's advertising approach) also had similar odds for the 2020 election that were quite far from 538.

The more salient counter-argument, I think, is that if prediction markets are functioning as advertised then this shouldn't matter.

If lots of Trump supporters are attracted by advertising to make expressive bets, this should draw smart money like blood draws sharks as informed investors snap up the free money...but this is contingent on smart investors actually being able to profit from this mispricing, which for the reasons in the post they may not be.

Adding some further comments on the performance of prediction markets in the 2020 election here - while the election is still ongoing, I think so far it seems to support the article.  Some numbers here are based on my fallible and sleep-deprived human memory, if anyone disagrees/has a better source I can update this.

Coming into the election, 538 had Trump at a 10% chance to win (saying words to the effect of 'Biden is in a very strong position, where he has several paths to victory even through a correlated polling error of the sort that happened to Clinton').  PredictIt and Betfair had Trump at 30-40%.

As the day went on, Trump did better than expected in several places (particularly Florida), and took a lead in several important states (PE, MI, WI), though with many mail-in and urban ballots remaining that were expected to be Democrat-favored.  At 11pm, 538 wasn't giving hard numbers but a couple places in their chat were talking about Trump being anywhere from a 20-50% chance to win and emphasizing that mail-in ballots were expected to shrink or remove his leads, while PredictIt and Betfair both had Trump at ~70% to win.

As of this writing on the afternoon of the next day, with no new surprises I am aware of except for the entirely as-predicted shrinking of Trump leads due to later-arriving ballots, 538 continues to say 'Trump is behind but could still manage an upset', while Betfair and PredictIt have swung from their previous ~70% to a ~20% that is in line with what 538 was saying last night.

While there are several interpretations you could place on these numbers, it rather looks to me like prediction markets overrated Trump from the beginning, heavily overreacted to Trump's early outperformance, failed to predict the effect of late-arriving ballots until it actually happened, and then swung around and dropped their probabilities heavily based on this predictable news, while 538 did a lot better.

538 forecast: 10% -> Trump gets positive news -> 20-50% -> predictable shrinkage in Trump lead -> ~20%
Prediction market forecast: ~40% -> Trump gets positive news -> ~70% -> predictable shrinkage in Trump lead -> ~20%

If we were dealing with an efficient market I wouldn't expect this to happen.  Then again, if we were dealing with an efficient market I would expect hedge funds to hire skilled analysts on 6-figure salaries to stay up all night tracking election results and arbitraging market swings like that.  Until that happens, I will keep an eye on prediction markets, but I will trust 538 over them.

I think there are misplaced parentheses in your equations. In section 3, they should be:

and so on in future equations. Essentially the parentheses should encompass the +10 term as well in all your equations. It seems your personal calculations were correct because the actual probability bounds that you gave match up with this version of the equation.

Thanks for an in-depth writeup!

Should be fixed now, thanks for the heads-up!

Promoted to curated: I expect I will be referencing this posts quite a few times. I've repeatedly in the past done Fermi estimates of how big the spreads on the popular prediction market platforms is, and this feels like a more thorough version of that. Thank you!

Yikes.  I did not know that, thank you!

There are several alternatives available to US residents. If you are willing to bet using crypto you can get large sizes and much lower fees than predictit. If you did not make substantial amounts of money (relative to your net worth) from the US election you made a mistake.

if we assume you are paying 35% income tax

This tweet claims "winnings are taxed as gambling income, and subject to a flat 25% rate". Is that the case, or are they taxed like normal income like the OP claims?

OP here: it is quite plausible that I am wrong, I am not a tax expert at all.  I'm surprised to hear that gambling income is a flat 25% rate - I've always heard about lottery winners losing ~half their money to taxes.  Quick Googling suggests that 25% might be the withholding rate rather than the tax rate: so if you make $1000 on gambling$250 will be withheld, but then you might actually owe more/less depending on your income the next time you do your taxes.  That is a guess based on a few minutes cursory Googling though, I do not entirely trust it.  If anyone can give a credible answer to this question I can update the article.

If you are going to try to make $via prediction markets, consult an actual licensed tax preparer, cpa, or financial advisor. You will likely have to set up a business of some sort (flat filing fee in most states in the hundreds of dollars range) in order to properly net out your costs against your winnings. The 2016 tax law changed the rules about hobby and gambling income to no longer allow you to deduct your costs, unless you itemize, which means unless you were already close to itemizing you end up paying 15% of your gross winnings, not of your net. I think you are mostly correct, especially regarding the 10% profits tax and the 5% withdrawal tax. But I just made$6k (on invested value of $20k) by betting on swing states, both pro and against Trump. The Upper Midwest swing states seemed like easy money and were mispriced, according to FiveThirtyEight. I also won with bets on SC and TX for Trump: I got the SC bets at 85%. Even considering fees, that means 8.5% for two months. This seems like absurdly easy money to me. I got greedy and bet on FL and OH and lost there, or my winnings would have been over$10k.

After the election was called, there were a number of places where you could get 10% in a few weeks (or 4% including withdrawal fees).

The main way to make money on this site is to avoid withdrawal fees as long as possible by cycling through a number of  low risk bets. It is kind of tedious and "picking up dimes in front of a roller coaster" to be sure.

I think you are mostly correct, especially regarding the 10% profits tax and the 5% withdrawal tax. But I just made $6k (on invested value of$20k) by betting on swing states, both pro and against Trump.

The Upper Midwest swing states seemed like easy money and were mispriced, according to FiveThirtyEight. I also won with bets on SC and TX for Trump: I got the SC bets at 85%. Even considering fees, that means 8.5% for two months. This seems like absurdly easy money to me.  I got greedy and bet on FL and OH and lost there, or my winnings would have been over \$10k.

After the election was called, there were a number of places where you could get 10% in a few weeks (or 4% including withdrawal fees).

The main way to make money on this site is to avoid withdrawal fees as long as possible by cycling through a number of  low risk bets. It is kind of tedious and "picking up dimes in front of a roller coaster" to be sure.