Picture the whole electorate as a dune of opinion heaped along one left-to-right policy axis: tall where many voters agree, thin where few do. You sculpt it here.
Each candidate can only feel, locally, which way to step to gain votes, so it does the one rational thing — it climbs toward more support. Anthony Downs's result: with two vote-seekers they always meet at the median voter, the point with half the electorate on each side — whatever the dune's shape. The median need not be the tall peak.
The dashed-gold ghost line is that median: the theory. The two tokens are the reality, forever crawling toward it.
The theorem is fragile. A third candidate leaves no resting place — a spoiler can win from a thinly-settled flank while the majority splits. And if distant voters abstain instead of settling, the center turns into a trap and candidates polarize outward.
The arena stalled mid-race. The lesson continues without it — everything you have already done is safe.