There are a couple of interesting threads on Cross-X.com that discuss the theoretical underpinnings of political process disadvantages. In particular, Ankur Sarodia has developed a mathematical model that seeks to demonstrate that certain political process disadvantages are not legitimate considerations when determining whether the affirmative plan should be enacted. In this guest post, Dylan Keenan—debate coach at Emory University and the Westminster Schools—provides a rebuttal to the Sarodia model.

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**#1 – About this rule of math.**

There’s no rule that says every x maps to a single value of y or z. Doing so assumes that y and z are functions of x. Not totally relevant to the argument, except that it is perhaps a way of arbitrarily choosing this over a model that would incorporate several impacts as different curves. Also, I hate math fallacies.

**#2 – This is just a model.**

I love math and I wish debaters incorporated more of it, but a model for policy comparison should be derived from the real world of policymaking, not the other way round. The fact is that we all know what it means for “passage” of the plan. It means it goes through congress. Immediately in zero time. Yes, an unrealistic assumption but one that serves us well. To say that because the word instantaneous is used here and that instantaneous in math has a meaning that precludes continuity (more on that in a second) is silly. It’s just word play.

“Instantaneous actions are undefined on a timescale. They are represented by open circles. So if you can agree that fiat should be instantaneous, then you would draw an open circle at the origin (where the x and y or x and z if you are using two biaxial graphs, or x,y and z if using a triaxial graph). The origin represents ‘right now’ and the positive x-axis represents the future.”

That’s where the jump is made. There’s no real reason this has to be the case. If the model ignores a relevant consideration, junk the model, don’t pretend something meaningful doesn’t happen.

**#3 – A little calculus will clear this up.**

Let me suggest a model that incorporates it.

First, I’m gonna refer to K impacts ‘Z axis’ as imaginary… and Policy impacts ‘Y axis’ as real, cause let’s be honest, that’s how it is.

Since the values of Y and Z are arbitrary you can (and logically should) say that Y and Z are identically zero for all X<0. It makes sense because the SQ is the baseline against which the plan effects are measured but changing this doesn’t really effect the model, you just have to change up the integral a little later.

What happens at zero?

x=0 represents passage of the plan. At zero, the moment of passage, there’s an open circle at the origin, since the SQ (which we assigned to zero on Y and X) is ceasing to be.

I’ll also suggest that there may be a second open circle at x=0 for some y and y values.

Where is that exactly? LIMIT AS x DESCENDS TO ZERO OF f(x), where f(x) gives the y and z values mapped from a given x value.

If you haven’t seen limits before, think about the version of the model I’m criticizing. The limit is what happens as you trace the curve of impacts back along the values of X towards x=0 and get arbitrarily close to 0.

Now, the calculus. I submit that the debate should be decided by a simple integral. The integral of f(x) over all values of x where f(x) is defined. (this end value is to account for the claim that discursive implications can stop at 1.5 hours or some arbitrary point). Obviously since the SQ goes back indefinitely into the past and is pegged to zero, we can say that the integral of f(x) over all negative x is zero.

And this works. Although f(x) is not defined at zero if you integrate the positive and negative values of x seperately and add them you get the integral I just mentioned. At the zero point (speaking of how I feel) x is undefined but taking oen, or any finit enumber of discrete values out of an integral operation, doesn’t change the value.

So, that’s how impacts work here. Now, back to politics. The reason politics was uncomfortable in the old model is that you were just tracing a net impact trying to use discrete values at various points of time. Integrating the condition over all points is more realistic because, for instance, a plan with initial big bad effects but long-term small effects might be beneficial. You know this by integrating over the long term.

The effects of passage are what induce the discontinuity. If you pass plan and that process of passage, condensed into an arbitrarily small time causes loss of capital and nuclear war then you go from an OK status-quo to an instantaneously bad situation. On the other hand if you don’t talk about politics, becuase you are doing something awful like going for biopower, or worse the cap K then, truthfully, the limit as x goes to zero from teh positive side of f(x) is zero. The reason is simple human capability. If the plan goes into effect arbitrarily close to the origin people need at least a nano-second to deal with the effects. After that nanosecond you start seeing impacts and the curve moves up or down along the Y and Z axes. Passage is a construct to compress a certain subset of those reactions into an instant, represented by the discontinuity.

Is my model arbitrary. Kind of. So is the other one. So, we return to the original point. What model accurately represents the world, not how can we create math to exclude things. In the real world capitalism rules, political capital matters and Indians killed the giant North American sloth.

**FYI**

It’s a little unclear what the net value referred to in the original model is, and that matters. Let’s say f(x), which maps x values to y and z values is a measure of all net impacts up to that point. So if y(5) — meaning the y value attached to time 5 — is positive then at that point all net effects including everything after passage is positive. So overall, adding everything since time 0 we’re better off. If that’s what f(x) does, then my model doesn’t work. I treat f(x) as the position at that point in time, relative to the SQ, but it doesn’t account for past times. In fact it could have discontinuities. It might be that the initial effect is a food spike so at every point up to some x, say x=5, things are neg. More people starving constantly. Then at time 5 i have some advnatage about a conference that will succeed because of the plan and once it succeeds no one will ever die again and humanity experiences eternal bliss (what like you’ve never heard a worse argument). Then suddenly f(x) jumps to the positive realm. Because that jump is a discrete instant it doesn’t effect the integral. But I figured I’d clear it up.

SahanGreat article, i think this site is going to be excellent in the future. although i agree with the article above i think it misses some points that were made in the original CX article.

First, math:

1. the original article made this way to complicated, you really need two axises, one representing time (t = t0 is the time when plan passes) and the other for impacts (i for simplicity sake) although it might be nice to separate out critical vs policy impacts if we were to do this then each separate offcase and adv would need their own axis (which is what we have in debate right now, each impact gets their own magnitude and timeframe). “i” can also be the implication or whatever do you impact calc and framework then turn it into an “importness factor” positive or negative.

2. the discontinuity is caused by a change in function, the first function is f1(?)=S.Q the second function is f1(?)= aff plan. The change between these functions takes place at t=t0 (above)

Now on to the fun stuff:

1. open-open connection at t=t0 actually allows all policy impacts to happen. During this time we ‘dont know’ what is going on, that is to say there is no time in which a change can occur and therefore, in his opinion, there is no time in which ‘stuff’ changes, which means politics links dont happen. This is wrong because we have an undifferentiable function (beacuse lim t–> t0- is not equal to lim t–>t0+) which means assumptions made at t0- are not the same as assumptions made at t0+, those assumptions could be anything but for the sake of this discussions assumptions about republicans attitudes pre-plan are different than those post plan. We debate what assumptions are still valid, (nuke war free world?) and therefore my politics scenario still works.

2. open-closed is a better but not by much, the same basic idea as above applies but one of the points is defined. There is still a discontinuity which means that assumptions changes and what not. now for those of you confused lets play this a different way where f1(obamas political capital)=PCE(political captial at election)-.005t, this equation is valid only in the s.q, after f2 (the aff plan) kicks in a new equation is needed to figure out obamas political capital based on the changes that have occurred from switching between f1(?) and f2(?). (if you want more math let me know but gatech does too much of that already so back to debate stuff)

3. Even if you dont buy any of the above arguments i can still get my politics links in your (the guy on Cross-x not you bill, your amazing) interpretation by winning that sudden passage or a liberal or conservative plan will piss people off and they wont complain about it until comes into play OR that the plan breaks a presidental commitment and since it occurs instantinously there is no chance for an apology which makes ____ not pass OR…

Finally T/ everyones right this whole discontinuity thing is weird, so from now on no more plans, lets all have stable critical advocacies so there is no t=to, its just prefer our existing movement or dont.