What happens if no vote is given in a single round?

When no one vote, nothing happens. The day count doesn't increase, the site's values do not decrease. It's being on pause.

No one is playing on parenting's site and it is still exactly the same as 5 minutes ago.

Half hour after I added the first image, it is still in the same state.

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If there are not sufficient votes, then the day counter does not increment, and no action is taken. If someone has previously voted, then their vote is locked until the votes are above the vote threshold.

The global minimum is 1, so there will never be a case in which any action can happen if no one votes.

Yes, because 0 votes would be below the vote threshold. According to the StackEgg FAQ:

What happens if not enough users vote for a voting round to count? Nothing. The day does not advance, and another voting round starts. All votes that have already been cast are kept, and the number of votes necessary in the new round is reduced by half.