2023-10 SNP elections: and the winner was ?

Wednesday, March 29, 2023
Deborda

SNP ELECTIONS

The first-round results counted only the 1^st preferences.

Preferences	%
	11	41	48
1st	Ash	Kate	Humza

 

The second round transferred only Ash’s votes: 7 to Kate and 4 to Humza.  So Hamza won, 52% to Kate’s 48%.  In effect, Ash’s 2^nd preferences were key, while all the 2^nd preferences of Kate and Humza were just ignored!

Maybe – we just don’t know – but maybe Kate, the 1^st preference of 41%, was also the 2^nd preference of 55%, and the 3^rd preference of only 4%.  While Humza, the 1^st preference of 48%, was perhaps the 2^nd preference of only 4% and the 3^rd preference of 41%. 

Preferences	%
	11		41		48
1st	Ash		Kate		Humza
	7	4	41	0	0	48
2nd	Kate	Humza	Ash	Humza	Ash	Kate
3rd	Humza	Kate	Humza	Ash	Kate	Ash

 

The rulers proposed by Jean-Charles de Borda in 1770 stipulate that:

in an election of n candidates (options), a voter may cast m preferences – so n > m > 1 –

and points shall be awarded to the

(1^st, 2^nd … n^th)

preferences cast, according to the following

(m, m-1 … 1)

points.  In which case, the count would be

Candidates	(Preferences and) Points			POINTS TOTAL
	1st	2nd	3rd
Ash	(11)    33	(41)     82	(48)   48	163
Kate	(41)  123	(55)  110	(4)      4	237
Humza	(48)  144	(4)        8	(48)   48	200
				600

 

and the winner would be Kate.  The conclusion is that a voting procedure should always take all preferences cast by all voters into account.

 

Article originally appeared on After Jean-Charles de Borda, 1733-99 (http://www.deborda.org/).