There would not be anarchy and ww3 - either the encumbent would go on until another round of elections was held, or an interim government would take over day to day business.
At some point an election would be held with mandatory voting because simply put, this one act of making a cross somewhere is the legitimation of the entire system.
If, however, people en masse boycotted the election even with mandatory voting laws, then you have a real crisis without precedence, I mean, that's the people declaring that the current version of democracy is now over. Who knows what would follow.
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I can read facial expressions. I did the test.