Underestimating Slope

Reading the short explanation for SlipperySlope on FallaciousArgument ('A leads to A^n'), let me think, that many arguments fail, because of the following pattern:

more B is good
more A leads to more B
therefore more A is good

(or the like, depends on A and B of course).

This reasoning is definitely not sound, if the dependency between A and B is not linear (assuming, that the goodness of A and B is the same).

That's an ends justifying the means problem... which is always a problem of economy. There is, in reality, no way to justify any means except by its ends, but doing so requires analysis of cost of means (including all 'side-effects') vs. utility of ends and a comparative analysis of alternative approaches. Your above statements don't even consider alternative approaches: More C leads to more B, therefore more C is good... but is C or A better?

Having more money is good.
Working as a mercenary, killer-for-hire leads to having more money.
Therefore obtaining more work as a mercenary, killer-for-hire is good.
And even better would be developing a culture where a killer-for-hire is never out of work...

This is aside from the discussion below, but is somewhat of another large fallacy extant in the same logic structure you just described.

In some cases, a significant amount of A may lead to insignificant changes to B in the beginning, but additional amounts of A may lead to much more B later (exponential growth; "priming the pump", "tipping point", etc.).

In other cases, more A may lead to more B in the beginning, but additional amounts of A may lead to smaller and eventually insignificant amounts of B (saturation).

This can be expression mathematically e.g. like

  B = A^r (direct polynomial dependency, if r>>1 a little bit A make much B, reverse if r<<1)

  B = A+p^A (late, but sudden increase e.g. if p<<1)

  B' = A'^r (dependency in the derivative)

That was my image of SlipperySlope at first: Not slope, that lets one fall deep down, but uneven slope which lets one stumble.

Examples:

Sending more fishing ships leads to more fishes caught, therefore send as much as you can. This ignores, that this will lead to diminishing returns if the resources become depleted.
Doing a little bit XP gains no or very few advantage therefore doing much XP gains no or very little advantage too. When in fact doing much XP, 100% at best, gains a large advantage (see AllOrNothing?, I know, that there is an XP page about it, but cant find it).

My example in fact was:

A little of A leads to a very few of B, therefore more of A leads to a little bit more of B.

Which is used in the argument as follows:

More advantage is good
More XP does not lead to more advantage
Therefore more XP is not good

I agree, that the example was not well chosen, because it requires the negation. I just wanted to use an XP example.

But anyway, I do not seem to be able formulate my thoughts about this concept clear enough. Let me think about it some more time.

There's definitely a fallacy around assuming that because a little of A causes some increase in B, then more A will result in more B. I would argue that performance related pay is one of these. Also see SelfSealingBelief.