Is this "laziness contest" joke a paradox?

Question

I stumbled across a seemingly paradoxical joke online that read:

"when your opponent doesn't show up to the laziness contest"

The joke is that you have already lost the contest by showing up to it and that your opponent (who has not participated) is the winner. I should note that the opponent has not shown up purely because they are lazy, not because of any other unforeseen circumstance.

I find it paradoxical because one can not win a contest if they are not participating in it.

Is this a paradox? If so, just as the Barber paradox illustrates Russel's paradox, I'm wondering if this joke can be matched to some mathematical paradox.

Edit: now that this question has been answered, I'd like to know for future reference why questions like these are so contraversial. At the time of writing, there are 4 close votes and a battle of up and down votes. This is more of a meta question, but a comment answer here would be fine!

Answer 1

I assume that the following is a rephrasing of the story.

1. For all contestant $C$, if $C$ is the laziest, then $C$ wins.
2. For all contestant $C$, if $C$ is the laziest, then $C$ doesn't show up.
3. For all contestant $C$, if $C$ doesn't show up, then $C$ loses.
4. For all contestant $C$, if $C$ loses, then $C$ doesn't win.

Then 1), 2), 3) and 4) are contradictory.

It reminds me of a famous joke: all integers are interesting! Indeed, assume that the set of uninteresting integers is nonempty. Then there is an integer that is smallest among the uninteresting ones. This is interesting!

Answer 2

There is nothing paradoxical to it. A competition tests the people who show up. For example, the best chess player in the world (Magnus Carlsen) didn’t compete in the recent FIFE world Championship, but that doesn’t mean the person who won (Ding Liren) is better than Magnus Carlsen.

Answer 3

It is not a paradox.

First, failure to show up for a contest is not automatic proof of “laziness”. Perhaps your opponent had an unexpected illness, family emergency, car crash, or something that prevented them from attending.

Second, if one or more contestants do show up for the contest, there is no reason to automatically disqualify them on this basis. Showing up would simply deduct points from their “laziness” score, and since it would apply to everyone who showed up, it wouldn't affect the relative ranking of the candidates.

There are other ways that a laziness contest could be implemented than simply checking attendance. For example, you could put all the contestants in a house for one day, and carefully measure how much time each one spends doing “productive” things (cooking, cleaning, exercising) versus “unproductive” things (sleeping, watching TV, checking social media). Whoever has the least “productive” time wins.

Perhaps the laziest person in the world is one who didn't enter the contest. But that doesn't matter. As Kamal Saleh pointed out, a competition only compares its participants. For all we know, there's a person somewhere who can sprint faster than Usain Bolt, who just hasn't gone to any Olympic tryouts. But until they actually compete, they won't get a medal for it.

So, I just don't see a logical contradiction or paradox here. There might be one if it were specifically a “not attending contests” contest instead a more vaguely-defined “laziness” contest.

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Edit: If this is a “not attending contests” contest, then the interpretation still depends on the rules of the contest.

1. You need not be present to win. In this case, your opponent who failed to show up wins. A strange contest, but not a logical contradiction.
2. You can win with a negative score. Compare to a stock-picking contest that happens to be held over a time period during which the stock market crashes and all contestants lose a lot of money. It is reasonable to declare the person who lost the least as the “winner”, even they would lose to a hypothetical do-nothing contestant who declined to invest and just stuffed their money under their mattress. Again, not a contraction.
3. The contest is literally unwinnable, because it adopts the traditional “must be present to win” rule of contests while also disqualifying anyone who is present. This case, which seems to be most in the spirit of the joke, is a type of self-referential paradox, similar to the Liar Paradox (“I am lying to you right now”) or Russell's Paradox (the set of all sets that do not contain themselves).

Answer 4

I can see two ways of interpreting the joke, and none of them is a paradox.

First interpretation: you won the contest, but everyone knows it's meaningless

You made the effort of showing up for the context. Your rival was too lazy to show up. Because they didn't show up, they didn't participate and couldn't win, so you won. But everyone understands that they are more lazy than you, so your title of "laziness champion" is meaningless.

This happens a lot in actual championships. For some reason, the strongest player couldn't attend the championship. Someone else becomes the official champion, but everyone knows they are not the strongest.

Second interpretation: they didn't need to be present to be a participant

Some contests allow candidates to register in advance. Then, they can be a participant even though they don't show up.

In many contests, not showing up would result in disqualification, in which case the missing participant would still be considered a participant, but they would be marked as disqualified and would not win the contest. For instance, if the contest consists in a series of 1vs1 matches, the missing participant might be paired to someone for round 1; then they would be marked as losing round 1 by forfeit, their round 1 opponent would be marked as winning by forfeit, and then the missing participant would be disqualified and wouldn't be paired in subsequent rounds. In the final listing, they would be in last position and be marked as disqualified.

However, in some contests, you don't need to be physically present in order to participate, as long as you completed the formalities of registration to the contest. For instance, imagine an inventors contest. Every participant is supposed to bring a demo of their invention on the day of the contest, showcase it during the day, and at the end of the day, a jury will announce the winner. If a participant registers, but fails to show up on the day of the contest, and presuming the contest rules do not contain a provision to disqualify contestants who don't show up, then this participant might still win the contest. They will not be there to help show their invention in the best light possible, and the jury might be reluctant to reward someone who didn't bother to show up, but if the invention is good enough, the missing participant might win anyway.

In the case of the laziness contest, if a jury is supposed to observe the participants during the day, and then decide who is the laziest, they might very well choose to reward someone for not showing up at all.