Liang Chen, College of Mathematics & Information Science, Wenzhou University, Zhejiang Province, China, 325000; Computer Science Department, University of Northern British Columbia, Prince George, British Columbia, Canada, V2N 4Z9; E-mails:; Partial work of this paper has been published in L. Chen, “Electoral College and Direct Popular Vote for Multi-Candidate Election”, Proceedings of the British Machine Vision Conference (BMVC 2010), pages 100.1–100.11. BMVA Press, September 2010; and L. Chen, “Stability as Performance Metric for Subjective Pattern Recognition?” Proceedings of 19th International Conference on Pattern Recognition (ICPR 2008), Tampa, FL, Dec. 8–11, 2008.


Subjective pattern recognition is a class of pattern recognition problems, where we not only merely know a few, if any, the strategies our brains employ in making decisions in daily life but also have only limited ideas on the standards our brains use in determining the equality/inequality among the objects. Face recognition is a typical example of such problems.

For solving a subjective pattern recognition problem by machinery, application accuracy is the standard performance metric for evaluating algorithms. However, we indeed do not know the connection between algorithm design and application accuracy in subjective pattern recognition. Consequently, the research in this area follows a “trial and error” process in a general sense: try different parameters of an algorithm, try different algorithms, and try different algorithms with different parameters. This phenomenon can be observed clearly in the nearly 30 years research of the face recognition: although huge advances have been made, no algorithm has ever been shown a potential to be consistently better than most of the algorithms developed earlier; it was even shown that a naïve algorithm can work, in the sense of accuracy, at least no worse than many newly developed ones in a few benchmarks.

We argue that, the primary objective of subjective pattern recognition research should be moved to theoretical robustness from application accuracy so that we can evaluate and compare algorithms without or with only few “trial and error” steps. We in this paper introduce an analytical model for studying the theoretical stabilities of multicandidate Electoral College and Direct Popular Vote schemes (aka regional voting scheme and national voting scheme, respectively), which can be expressed as the a posteriori probability that a winning candidate will continue to be chosen after the system is subjected to noise. This model shows that, in the context of multicandidate elections, generally, Electoral College is more stable than Direct Popular Vote, that the stability of Electoral College increases from that of Direct Popular Vote as the size of the subdivided regions decreases from the original nation size, up to a certain level, and then the stability starts to decrease approaching the stability of Direct Popular Vote as the region size approaches the original unit cell size; and that the stability of Electoral College approaches that of Direct Popular Vote in the two extremities as the region size increases to the original national size or decreases to the unit cell size. It also shows a special situation of white noise dominance with negligibly small concentrated noise, where Direct Popular Vote is surprisingly more stable than Electoral College, although the existence of such a special situation is questionable.

We observe that “high stability” in theory indeed always reveals itself in “high accuracy” in applications. Extensive experiments on two human face benchmark databases applying an Electoral College framework embedded with standard baseline and newly developed holistic algorithms have been conducted. The impressive improvement by Electoral College over regular holistic algorithms verifies the stability theory on the voting systems. It also shows an evidential support for adopting theoretical stability instead of application accuracy as the primary objective for subjective pattern recognition research.