After Jean-Charles de Borda, 1733-99

CHINESE FILM STARS (The first demonstration of electronic voting was in Beijing.)

中国的影星

In consensus voting, we seldom if ever choose only one individual/policy option. Compromise is the key. So we always try to vote for more than one candidate/option, and either select more than one individual – a boss plus a deputy, say – or choose a composite policy of the two leading options.

To find China’s most popular film stars, maybe four of them, 18 students were given a short list of the 10 top actors. They were asked to cast their preferences on their smart phones – the programme is on www.debordavote.org – a 1 for a 1^st preference, a 2 for a 2^nd, a 3 for a 3^rd, and so on.

In the count, the lowest preference cast gets 1 point; the one but last gets 2; the two but last gets 3, etc. So if a voter casts a full ballot, his 1^st preference gets 10 points, his 2^nd gets 9… but if another casts only six preferences, her 1^st preference gets just 6 points, her 2^nd 5, her 3^rd 4, and so on.

Points per a full ballot = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55

No of voters = 18

Total number of points that could be cast = 18 x 55 = 990

Maximum score for any one actor (in full ballots) = 18 x 10 = 180

Minimum score for any one actor (in full ballots) = 18 x 1 = 18

Some people cast only partial ballots, and the total number of points cast = 815.

The filmstars 影星		Preferences											Points
The filmstars 影星		1^st	2^nd	3^rd	4^th	5^th	6^th	7^th		8^th	9^th	10^th	Points
成龙	Chéng Lóng	8	1	1	4	-	-	2		1	-	1	114
邓超	Dèng Chāo	1	3	1	-	3	2	-		-	3	2	75
范冰冰	Fàn Bīng Bīng	-	1	3	-	2	-	-		2	1	6	53
巩俐	Gõng Lì	1	1	1	3	1	1	4		1	1	1	75
李宇春	Liú Dé Huá	2	2	2	5	2	2	1		-	1	-	100
李宇春	Li Yū Chún	-	2	1	-	-	2	2		1	4	2	57
徐静蕾	Xú Jìng Léi	-	1	4	-	2	4	-		3	1	1	74
徐铮	Xú Zhēng	2	4	1	1	1	1	1		2	1	-	94
张国立	Zhāng Guó Lì	2	1	2	2	3	1	3		2	1	-	85
张蔓玉	Zhāng Màn Yù	2	2	2	3	1	1	1		2	1	1	88
									Total points cast:				815

The second table lists the film stars in their order of popularity. The winner is成龙. The next four are fairly close together; then there’s a gap before three actors all on 75 or 74 points; and lastly come the two least popular actors. But given this gap, it’s probably wiser to say that, for these 18 students, “The most popular actors are the top five: 成龙，李宇春，徐铮，张蔓玉和张国立.”

The filmstars 影星		Points	Place	The filmstars 影星		Points	Place
成龙	Chéng Lóng	114	1^st	邓超	Dèng Chāo	75	= 6^th
李宇春	Liú Dé Huá	100	2^nd	巩俐	Gõng Lì	75	= 6^th
徐铮	Xú Zhēng	94	3^rd	徐静蕾	Xú Jìng Léi	74	8^th
张蔓玉	Zhāng Màn Yù	88	4^th	李宇春	Li Yū Chún	57	9^th
张国立	Zhāng Guó Lì	85	5^th	范冰冰	Fàn Bīng Bīng	53	10^th

And the second demo was in Xuzhou.

In Xuzhou, thrre were only eight participants, but they all submirtted full ballots. And if a voter casts a full ballot, his 1^st preference gets 10 points, his 2^nd gets 9… but if another casts only three preferences, her 1^st preference gets just 3 points, her 2^nd 2, and her 3^rd 1 point.

Points per a full ballot = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55

No of voters = 8

Total number of points that could be cast = 8 x 55 = 440

Maximum score for any one actor (in full ballots) = 8 x 10 = 80

Minimum score for any one actor (in full ballots) = 8 x 1 = 8.

The voters’ profile shows who got what. Gõng Lì, for example, got lots of 2^nd preferences, a couple of 5^ths, and just one 10^th preference. Now a 2^nd preference gets 9 points, a 5^th gets 6, and a 10^th gets 1, so Gõng Lì gets a total of 5 x 9 + 2 x 6 + 1 x 1 = 45 + 12 + 1 = 58.

The filmstars 影星		Preferences											Points
The filmstars 影星		1^st	2^nd	3^rd	4^th	5^th	6^th	7^th		8^th	9^th	10^th	Points
巩俐	Gõng Lì	－	5	－	－	2	－	－		－	－	1	58
徐铮	Xú Zhēng	1	2	1	1	－	1	2		－	－	－	56
李宇春	Liú Dé Huá	1	－	2	1	－	2	1		－	1	－	49
章子怡	Zhang Zi Yi	－	1	2	1	1	1	－		1	－	1	47
徐静蕾	Xú Jìng Léi	1	－	－	2	2	－	－		2	1	－	44
张蔓玉	Zhāng Màn Yù	2	－	1	－	－	1	1		1	－	2	42
张国立	Zhāng Guó Lì	1	－	－	－	1	2	2		1	1	－	39
成龙	Chéng Lóng	2	－	－	1	－	－	1		－	2	2	37
邓超	Dèng Chāo	-	－	2	－	1	－	1		2	1	1	35
李宇春	Li Yū Chún	-	－	－	2	1	1	－		1	2	1	33
									Total points cast:				440

So the most popular got no 1^st preferences at all! But because she got so many 2^nd preferences, she nevertheless comes out on top. The other conclusion is that the two top actors, Gõng Lì and Xú Zhēng, are very close; then there’s a gap of 7 points…. and everybody else follows 2 or 3 points behind the next. So the conclusion of these students is that Gõng Lì and Xú Zhēng are China’s two best actors.

If, however, a plurality vote had been used – (the sort of system which the British use in their elections) – the outcome would have been a draw between Zhāng Màn Yù and Chéng Lóng, two of the least popular film stars!