Is there a logical fallacy in the following statement?

Agree w/ Mr Walker and Dr. Bo.

Anyone with serious intellectual skills knows that we can and should question anything that needs to be questioned. That doesn't mean that we should be paranoid, just that we shouldn't accept all accepted wisdom at face value. Peace to all.

Good question, Martin Smyth!

I am being a bit pedantic, but

Person A: "We should question the results of a vote when it's possible that the vote has been tainted."

Via a reductio, it is possible that any vote has been tainted, so therefore, we must question the results of every vote. Either this is a absurd or it is meaningless, in that it would just be more clear to say "we should question the results of all elections."

Now to your question,

Person B: "There is no point in questioning the results of a vote since we'd have to question the results of every vote in living memory."

In one sense, they are alluding to what I had said. This means that all votes could be tainted. Their error is that just because all votes (past, present, and future) could be tainted, it doesn't follow that there is no point in questioning the results of any given vote. The general fallacy is the non-sequitur. Perhaps more specifically, this would be the Nirvana Fallacy<>. The ideal solution might very well be to question every vote in history, but since that it an impossible task (practically speaking), we can't ignore that questioning any one election would be good enough or at least an improvement.

From Dr. Bo's Logically Fallacious:

Slippery Slope
(also known as absurd extrapolation, thin edge of the wedge, camel's nose, domino fallacy)

Description: When a relatively insignificant first event is suggested to lead to a more significant event, which in turn leads to a more significant event, and so on, until some ultimate, significant event is reached, where the connection of each event is not only unwarranted but with each step it becomes more and more improbable. Many events are usually present in this fallacy, but only two are actually required -- usually connected by “the next thing you know...”

Logical Form:

If A, then B, then C, ... then ultimately Z!
Example #1:

We cannot unlock our child from the closet because if we do, she will want to roam the house. If we let her roam the house, she will want to roam the neighborhood. If she roams the neighborhood, she will get picked up by a stranger in a van, who will sell her in a sex slavery ring in some other country. Therefore, we should keep her locked up in the closet.
Explanation: In this example, it starts out with reasonable effects to the causes. For example, yes, if the child is allowed to go free in her room, she would most likely want to roam the house -- 95% probability estimate[1]. Sure, if she roams the house, she will probably want the freedom of going outside, but not necessarily “roaming the neighborhood”, but let’s give that a probability of say 10%. Now we start to get very improbable. The chances of her getting picked up by a stranger (.05%) in a van (35%) to sell her into sex slavery (.07%) in another country (40%) is next to nothing when you do all the math:

.95 x .10 x .0005 x .35 x .0007 x .4 = about 1 in 25,000,000.

Morality and legality aside, is it really worth it to keep a child locked in a closet based on those odds?

I want to thank all of you for your responses, still pretty new to fallacies and from first glance, I kept thinking it was a red herring as it is alluding, but again thank you all and if I could upvote I would, but I need more points for that.