The conceptual framework behind the option to reject all is that it brings voters' consent into the electoral process.
A democratic government is supposed to be created by the consent of the governed, but in the current electoral process there is no meaningful way to withhold consent, so consequently consent cannot be meaningfully be given either.
With a viable option to reject all on the ballot, voters are now able to meaningfully withhold consent and so therefore are giving their consent when they vote for any candidate.
The reason why at least 50% must choose to reject all to trigger a new election is that if you vote for any one candidate, your consent to be governed by the eventual winner, whether you voted for him or not is assumed.
So it quite different from a write in candidate, or spoiling a ballot (which nothing more than an abstention)
The way I describe it is that currently our electoral model is simply 'lead, follow, or get out if the way' and this is why many people feel powerless within our so called democracies, they are currently stripped of the democratic prerequisite of being able to give and withhold their consent in elections.
In my view its THE key reform required to shift the balance of power away from political parties (and the special interests that control them) into the hands of voters. Currently the electoral system begets nothing more or less than an elected oligarchy, with only constitutional restraints and independent institutions holding them somewhat in check. Voters are relatively powerless in this system, and are very much the junior partners at the table, though are heavily patronised as being more powerful than they are, but this charade is fast becoming impossible to maintain.