Is Steem paying for Groupthink? The Game Theory of Steem, Part 3
For those who just joined us, we're looking at an imaginary problem where a newspaper is trying to incentivize subscribers to vote on beauty contest entrants, and we're trying to work out the best incentive structure.
In Part 2, we showed that paying a flat fee for every vote may lead to random voting; in this installment, we'll take a look at doing something a little bit more sophisticated. We'll also introduce a notion of Nash Equilibrium, and show that the question of paying people to vote may actually lead to some weird behavior.
The problem with the first approach was that the incentive was not correlated to the quality of the vote. What we'd really like to do is pay people who submit "good" votes more than we pay people who submit "bad" votes. The problem is that a priori (that's economist-speak for "before we start"), we can't tell the difference between good and bad votes.
Let's try something that sounds clever: let's collect all the votes, find the winning beauty contest entrant, and give $10 to everybody whose vote was for the winner. This is starting to look reminiscent of Steem! It turns out that this is called a "Keynesian Beauty Contest." Yes, that economist with the weird lips (that everybody around here loves, I'm told), John Maynard Keynes, came up with this analogy between the stock market and a beauty contest in which people are paid money if their vote turns out to be for the winner. I'll let people debate the validity of the analogy in the comments to this article; we'll just stick with the beauty contest here.
I'll build a concrete example. To keep things simple, let's have voters choosing between two beauty contest entrants:
Aww, how cute! A puppy (P) and a kitten (K)! So the first two components of our game specification are in hand already: we have players (voters, I'll also call them agents), and we have actions (vote P or K). To fully specify a game, we need to define the 3rd part: payoffs.
Our payoff functions will have two components. The first is "idiosyncratic": each person has a personal preference for P or K, and in principle the strength of each person's preference could be different. So we'll use the letter vi to denote this preference (v stands for "value"). If voter i prefers P, then vi represents how much voter i wants to see P win (alternately, if i prefers K, then that's the strength of i's K preference). Think of vi as the maximum amount of money that i would pay to change the result from K to P. Of course, the second payoff component is the monetary reward for picking the winner; just like in Part 2 we'll call this p.
Now we have all we need to define the utility function for agent i. We'll write ai to denote agent i's vote, and a-i to denote everybody else's vote. If agent i is a puppy-lover, here is the utility (payoff) function:
Just so we're absolutely sure we know what we're doing, let me pick that apart line-by-line:
- If my favorite wins and I voted for it, I get paid and get happy.
- If my favorite wins but I didn't vote for it, I don't get paid but at least I'm still happy that my favorite won.
- If my favorite loses, but I voted for the winner, I'm not happy but at least I get paid.
- If my favorite loses, but I voted for it anyway, I'm neither happy nor paid.
See where I'm going with this? It looks like paying the winners could actually be setting up a perverse incentive for people to lie about their favorite. Let's analyze this formally.
First, let's assume that there are a lot of voters, and the margin of victory is at least 2 votes, so that no single voter can switch their vote and change the outcome. This will usually be true, and it helps focus on the issue of perverse incentives. Before I go any further, let's chew on the following definition:
Definition: Nash Equilibrium. A Nash Equilibrium (NE) is a collection of votes in which no voter wishes they could individually switch their vote to something else.
This is the intuition: First, we let everybody vote. Then we go up to each voter in private, show them the result, and ask them if they would be better off having voted for something different. If every person says "nope, I'm happy with how I voted," then we call that a Nash Equilibrium. With this definition in hand, I'm going to make a claim:
Claim: When p > 0, regardless of how strong peoples' individual preferences are, there are exactly two Nash Equilibria: one where everybody votes P, and one where everybody votes K.
How can this be true? What we're saying is that I could like puppies SO MUCH - my vi for puppies could be a billion - but still I'd prefer to vote for kittens. Why? We need to look at the payoff function to understand it! Suppose kittens win the contest. That means we're living in the last two rows of the payoff function. Well, that makes it simple! I could stick to my guns and vote P, but then I'd get a payoff of 0. Or, I could write down K instead, vote with the crowd, and I'd get paid money! Notice that vi does not show up in the last two rows; if puppies don't win, it doesn't make any difference how much I like them. I have a strong incentive to vote for kittens, even though I actually want them to lose.
Now let's bring this back to Steem. Steem works by paying people to vote for the winners, just like in the kittens/puppies game. At first glance, this seems to make sense - the winners should be the highest-quality, right? But the story of puppies and kittens highlights a subtle issue: paying people to vote for winners can skew the incentive away from voting for quality, and towards voting with the crowd and participating in groupthink.
By all means, the Steem system is a lot more complex than our toy puppies/kittens example, so the story isn't done yet. We have a lot left to analyze! I haven't even begun to talk about short-term versus long-term payoffs, and we haven't considered the fact that voters in Steem have multiple votes, and I haven't even touched on the question of what incentives the content-creators experience.
Also, let me give credit where credit is due: I brushed up on this material by reading this article and looking through these lecture slides by Muriel Niederle at Stanford University. I also just ran across this related article by @smooth: Voting is a popularity contest.
My other articles you may find interesting:Part 1 of the game theory series: Introduction
Part 2 of the game theory series: Beauty Contests
And now, before I go, I'll pose a discussion question: Why should we be skeptical of my simplified puppies/kittens example?
Nice post. Thanks for alerting me to it with the comment on my post. It's getting harder and harder to find all the hidden gems on Steemit these days.
That is unavoidable in the current system design, due to the one-size-fits-all reputation system, i.e. each user will have different priorities but the design of the system doesn't accommodate such degrees-of-freedom.
If some of the voting power shares your preferences, that content will rank higher than content that interests none of the voting power, but assuming that interests are reasonably diverse then ranking will be more or less uniform and uncorrelated to individual preferences. So thus more or less in order for any content to rise up, it must be a groupthink effect.
An improvement would be some algorithm which allows each grouping of like-minded interests to have their own separate ranking computation. The monetary reward algorithm would also need to change, so as to reward content that ranks highly in any grouping.
Well, I truly believe that we're in an awkward, soon-to-pass phase here where we get $35,000 makeup tutorials immediately followed by $10,000 parody makeup tutorials. Nothing has ever been done on a socialedia blockchain, so the first time anything happens it's going to generate a lot of hype.
I suspect we need a better sub-steemit structure, more like reddit, so that interesting content is easier to find. You should read the recent rant about this by @jacobt . His proposed solution is pretty crude, but I think he's probably on the right track.
I think perhaps I see a way to make Steemit much better than Reddit by making a change along the lines I suggested, but I am not sure yet. I am working on the details. I'll probably make a blog post if I am able to come up with a ranking algorithm I feel is reasonably solid.
Done:
https://steemit.com/steemit/@anonymint/improving-steem-s-rankings-to-cater-to-diverse-content-preferences
Thanks for checking it out! Part 4 is up!
Part 5 is up!
Your article inspired me to think a bit about the cost function in the incentivation system, leading to the conclusion that steemit will be soon completely overrun by bots. If you are interested in this, you can read the article here: https://steemit.com/created
"Why should we be skeptical of my simplified puppies/kittens example?"
Great post. So the utility function assumes there is no value in voting your preference. There is value assigned to the payout and the outcome, but what about the act of voting your conscious. I'd propose that in addition to your vi (value if your preference wins) and p (payout), there is additional value to your voter or "agent" in simply having voted their preference. This is why people vote for third party candidates in US presidential races, right? If we introduce another variable, say "ci" for how much the voter values voting there conscious, I think you potentially end up with multiple Nash Equilibrium, particularly where ci is greater than p.
DING DING DING!!! Everybody upvote this guy! Yep, that's the answer I was hoping somebody would give. Ignoring your "conscience-value" ci is the trick that lets us claim uniqueness of Nash Equilibria, which makes the result sound much more convincing than it should be.
I don't have time to think about it now, but it might be interesting to see if including ci could lead to anything weird, unexpected, or perverse. I'm fairly certain that in the simple two-choice model, ci would only make our equilibria look better, but sometimes these things can surprise.
Thanks! We could call "ci" the integrity variable.
@biophil thoughts?
this has also been a worry of mine about steem, since i invested, if steem is growing this much and most posts that gain traction around here seem to be "circle jercs" or "i love steem so much" posts, and people are posting to post to gain from it, we´ll be stuck with not a social media of good quality content but of cat pics, boobs and yeah basically "the internet".... p.s. i am still a steem investor (i became afraid of posting anything relatively negative about steem after being bullyed and downvoted on by a whale for a post on economic history, bubbles and the need for precoution in investing yesterday...)
Hi @eythor, I'm sorry you were bullied. Yeah, I purposely made this post's title provocative so I could try to draw out some whales. We'll see if it pays off...
i deleted... dont have the balls to say anything else than steem´s economic model is great, and in the long term will be GREAT full of boobs and cat pics. :) and moneyz for all
ohh tought i deleted my comment, but i´m drunk... so :)
These games are very interesting to me. (P)
One reason we may be skeptical of the simplified puppies/kittens example is that I think you are alluding to a simultaneous Nash equilibrium, whereas with Steemit people will vote at different stages, so we have to account for the aspect of taking turns and time element. Steemit is full of 'sub-games' like the one you describe between Puppies and Kittens where previous actions affect immediate and future payoffs.
Also, the Nash Equilibrium can be deduced but people are not always rational decision makers. People tend to have 'bounded rationality' so with the mass of information on Steemit they may not vote optimally.
Yep, agreed on all counts. I'm glad you brought up the bounded rationality thing; in fact that may be the topic of my next article because it's such a natural extension here. K-level reasoning and all that.
At first glance, I think the "vote-with-the-crowd" result will still hold up - even when we take bounded rationality and game timing into account. We shall see...
@biophil asks: "Why should we be skeptical of my simplified puppies/kittens example?"
The obvious answer is: "Everyone knows that puppies are better, and therefore the correct choice."
However, more seriously I would venture to guess the complications beyond the dichotomous choice, coupled with the visibility of choices to vote on based on appearance/availability altered by previous voters (which are also displayed and create influence) cause a situation that makes the simplified example (although educational) not applicable in full to #steem.
Admittedly, my reasons may be wrong, but may account for steem paying for groupthink.
The superiority of puppies not withstanding, I'd actually argue that being able to see other people's votes makes Steem more susceptible to groupthink. If somehow we didn't get to see people's votes until after payouts were made, I suspect we'd be more likely to vote for stuff we actually like, rather than vote on stuff just because other people are voting on it.
But I do like that you mentioned the oversimplified dichotomy; I wouldn't be surprised if that ends up playing a role.
Also that all votes are not equal because of investment incentives to have more Steem Power to have greater sway impacts visibility and payouts, which is also a differentiating factor not found in the simple example.
Thank you though for bringing up this topic.
I posted the same thing before I read this
Part 4 is up!
I suppose that one possible response is that whales have an incentive to preserve the value of their investments, and the best way to do that is to promote a system of fair voting and promote the integrity of the system. We have already seen changes to the curation rewards system which negatively impacted a lot of whales in terms of steem power, but you could argue it positively impacted the whales in terms of future value of their steem power, since their accounts only have value in so far as this is seen as a legitimate enterprise.
Yeah, I'll be looking at that in upcoming installments. I have a feeling that it's going to prove difficult to analyze; it's akin to the arguments for the original Proof-of-Stake coins like PPC and Nxt: put system security in the hands of the people who have the most to lose.
It's one of those arguments that has a logical ring to it, but it's not obvious to me that awareness of long-term consequences always leads to good short-term decisions. I'll definitely take a crack at it, though!
Keep on burninating!
It lacks, I think, the direct circularity of proof-of-stake where who owns the coins is determined by consensus and consensus is determined by who owns the coins. There is a different sort of circularity though, perhaps more akin to proof-of-work where security goes to zero if value goes to zero and vice-versa. In any case, I look forward to your analysis.
The one-size-fits-all ranking system (c.f. my other reply to smooth below) makes it impossible for whales to act rationally, because they can't compute a set of votes which would reflect their individual preferences for quality which might be shared with other like-minded users.
Thus as far as I can see, the system disincentivizes the whales from participating in voting, for they will come to see that either they become one dysfunctional groupthink monolith or they more or less effectively nullify each others votes in terms of anything other than a uniform ranking which is functionally equivalent to no ranking.
Yes, that's right.
you wanna see group think in action?
study this case user @lauralemons
its a gold mine, whatever perspective you take.
Amazingly weird shit happening with that user, or society is 10 times as fucked up as I previously thought
Fascinating.