User:Volunteer Marek/RfATermLimits


 * Main benefit of term limits actually obvious - get to remove bad admins and correct "mistakes" made at RfA based on additional information: behavior after confirmation
 * Desysopping can happen in some circumstances but anyone with half a brain who's been around for more than a few months knows how difficult it really is even in obvious cases.
 * "Open to recall" is an exercise in bad taste and hypocrisy.
 * Aside from very particular positions and rare circumstances term limits are the norm in RL.
 * So weird that it's such a no-go given how much of a no-brainer it is. But ok... think about it some more
 * Selfish vested interest - obvious and probably the correct explanation.
 * "It was proposed before and failed" - not an actual argument but simply an obnoxious shouting to shut down the discussion
 * "RfA is vicious enough as it is" - Premise is true. But would imposing term limits actually make this worse? Common sense says the opposite.
 * "We don't have enough admins" - accept premise (even if disagree). But this is related to above. Is lack of admins a supply or demand problem? If imposing term limits made RfA nicer, then RfA nicer would make for more nominations, which would make for more admins.

Focus here on the last two. What would the effect of imposing term limits be in practical terms? Can you get have your cake and eat it too: can you make RfA nicer AND have more admins if you impose term limits?

Yes. That's partly why every other half-functioning institution imposes them.

Model
Suppose that any potential admin candidate can either turn out to be a "Good Admin" or a "Bad Admin" (of course in reality could be in between but this doesn't matter here). A "Good Admin" will contribute value added of G to Wikipedia every period they keep their adminship. A "Bad Admin" will subtract value added of B from Wikipedia every period they keep their adminship. For simplicity (can relax later) suppose these costs/benefits are symmetric so that G=-B=X. If the candidate is not confirmed then the value added of this non-confirmation to the project is 0.

Let p be the subjective assessment of an RfA voter as to whether a particular candidate is one of the "Good" or the "Bad" ones. We could consider voters who are "risk averse" (the expected value of a candidate's contributions if approved needs to be sufficiently positive) but most of the point can be made with just "risk neutral" voters.

1 Year Term

Expected value is pX-(1-p)X. Choice boils down to whether this is > or < than 0, or in other words, whether or not p is greater or less than 1/2 (the one half comes from the assumption of symmetry, otherwise it'd be some other value between 0 and 1).

No Term Limits

More complicated (not really). Let b<1 be the "discount factor" which represents the probability that a particular editor (admin) may quite the project in the future and also "intrinsic rate of time preference" (basically impatience and the fact that we weight the future less than the present). Assume that the horizon is infinite (the fact it's may not be is already captured to a large extent in the fact that b<1). Then the present value of a "Good" candidate, if confirmed is Xb+Xb^2+Xb^3+Xb^4+...=X/(1-b). Likewise the present value of a "Bad" candidate, if confirmed is -X/(1-b). Note that with no term limits the choice of a "Support" or "Oppose" vote boils down to exactly the same thing as in the case of 1 Year Term; is p greater or less than 1/2.

2 Year Term Limit

Here we assume after the first year of adminship, the confirmed candidate fully reveals themselves to be either the "Good" or the "Bad" type. Again, could complicate this by assuming that this kind of information comes in gradually or whatever, but this has no impact on the basic results. Hence any "Bad" candidate will be desyssoped after one year. This means that the value added contribution of a "Good" candidate is still X/(1-b), but the harm done by a "Bad" candidate is just X. Hence the expected value of a candidate under a 2 year term limit is pX/(1-b)-(1-p)X. This is positive (the RfA voter will vote "Support") if p>(1-b)/(2-b)

Note first implication. If b=0 then the 2 Year Limit choice is same as the No term limit choice. This of course makes perfect sense. If b=0 this means that RfA voters are not forward looking and only care about the next year.

As b goes to 1 (RfA voters are infinitely patient) then p goes to 0, which means that "almost all" candidates get approved. This also makes perfect sense. With term limits you can always remove a "Bad" candidate after one year, and since you're very very patient that one year of bad adminship is insignificant compared to all the periods in which the potential candidate could make "Good" contributions (if that's their true type). This highlights the implicit Loss Function at work here.

Loss function

There are two possible errors that can be made by RfA voters.

Type I error - accepting a "Bad" candidate

Type II error - rejecting a "Good" candidate

The existence of term limits - the ability to remove folks who prove themselves incompetent or unworthy or whatever - lowers the costs of Type I error. In the limit, as you get infinitely patient RfA voters, the cost of Type I error goes to zero (hence they accept almost all candidates). It does not change the costs of Type II error.

Implication - introduction of a two year term limit (or even 1 year limit actually) will increase the acceptance rate. In this sense imposing term limits WILL make RfA "nicer".

Will the costs/benefit go up or down?

Need to describe where p comes from. Here p is the subjective assessment of the median RfA voter of the probability that a particular candidate is "Good". Assume that this voter has some prior (implicitly we set this to 1/2 here - a priori a candidate is judged just as likely to be bad as good. Again can change this later) and then receives a "signal" about the candidate. This "signal" could be comments by others, the candidate's statement, pure randomness, etc. For simplicity assume a logistic formula. (Also we could make these signals idiosyncratic to individual voters which would gives us a distribution of votes but again, doesn't matter)

p=exp(v)/(1+exp(v) where v is the signal.

Of course we need to somehow introduce a difference between the good and bad candidates. So assume that for "Good" candidates, v is normally distributed with mean uvg and variance sigma, while for "Bad" candidates, v is normally distributed with mean uvb and variance sigma (could assume different sigmas, again, doesn't much matter), with uvg>uvb. In other words, on average a "Good" candidate will send a good signal and a "Bad" candidate will send a bad signal to the voters. But some "Bad" candidates will manage to send a good signal, through chicanery, dishonesty, ass kissing and sheer luck, and some "Good" candidates will send a bad signal just through clumsiness, "wrong politics", and dumb luck. The inaccuracy of the signals is what leads to the two types of error described above.

With the above formula for p, under no term limits the RfA voter will "Support" a candidate if exp(v)>1 or v>0. Again the zero is the result of assuming that G=-B=X and that there is no risk-aversion. The frequency of Type I and Type II error is illustrated below.