Strategic Voting and Coalitions

Its archives show that “the voters found how to manipulate the Borda rule: not only by putting their most dangerous rival at the bottom of their lists, but also by truncating their lists”

I don't understand how putting your enemy at the bottom is manipulation. You, ostensibly, really don't want your diametrically opposed enemy winning. Truncating the lists though probaby affects point assignment.

To achieve this end result deliberately, voter 1 must be aware of the preferences of all other voters, and of the workings of the electoral system.

Borda attempts to give equal weight to choices but the weight of each choice is dependent on the number of candidates on the ballot.

Dowdall assigns a weight of 1/P where P is the position in the ballot starting with 1.

Borda's weights form a linear descent of importance, while Dowdall weights form a 1/x descent. Relative importances are quashed and spread across the curve based on how many ballot options exist.

On average, the Dowdall rule gets a conflicting outcome to PBV only 4.9% of the time, as compared to 28.8% for the Borda Count, and a different outcome to SNTV in only 8% of cases as compared to 36.2% of the cases with the Borda Count.

Basically Borda has a linear scale which changes the distance from the highest and lowest candidates based on candidate count, while Dowdall's 1/x rule ensures the measurement distance from highest to lowest is always the same regardless of candidate count.