政治候选人动力学中的蓝天分岔
A blue sky bifurcation in the dynamics of political candidates
AI总结：
用微分方程形式化政治候选人立场动力学，发现选民忠诚度减弱时候选人最终位置因蓝天分岔发生不连续跳跃。
摘要：
政治候选人常常机会主义地改变立场，以期获得更多选票。当仅有两名候选人时，各自的最佳策略通常是向对方靠拢。这最终导致两名持趋同观点的中间派产生。然而，当足够多的选民弃权（不执行），而不是投票给不代表其观点的中间派时，向对方靠拢的策略便不再是最佳选择。这些观察结果已以多种方式被多次形式化。我们自己的形式化基于微分方程。从这些方程得出的令人惊讶的主要结果是，随着选民对其候选人忠诚度的减弱，最终的候选人位置可能会发生不连续的跳跃。其背后的数学机制是蓝天分岔。
英文摘要：
Political candidates often shift their positions opportunistically in hopes of capturing more votes. When there are only two candidates, the best strategy for each of them is often to move towards the other. This eventually results in two centrists with coalescing views. However, the strategy of moving towards the other candidate ceases to be optimal when enough voters abstain instead of voting for a centrist who does not represent their views. These observations, formalized in various ways, have been made many times. Our own formalization is based on differential equations. The surprise and main result derived from these equations is that the final candidate positions can jump discontinuously as the voters' loyalty towards their candidate wanes. The underlying mathematical mechanism is a blue sky bifurcation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
