There are lots of voting system criteria that have been described, but I have 
not seen this one - or any one like it - described before.

Bullet-voting prohibition Criterion:
"A voting system should not be constructed in such a way so that it is both 
legal and rational for a voter to fill in a ballot with only one party or 
candidate name, so that the voter refuses to order by preference all candidates 
that are not his first preference."

Since FPTP enforces bullet voting, it obviously fails the BVP criterion. In 
Approval voting, it is legal to vote for only one candidate, so it fails also. 
In score voting, it is legal to give 99 points to one candidate and 0 points to 
all others, so it also fails. All other voting systems (that I can think of 
right now) can be made compatible with this proposed BVP criterion by adding a 
rule that the voter must supply at least 4 (or whatever number sufficiently 
high) most preferred candidates, otherwise the vote is spoiled.

Why do I consider the BVP criterion necessary? Two reasons:
1. It makes impossible some strategies that could otherwise be used by voters 
who are in favor of one of the top-2 parties, and want to ensure a two-party 
duopoly, even after the FPTP system is scrapped. I hold it for necessary that 
any change of the voting laws that scrap FPTP should not only mandate a better 
voting system, but also make it impossible for hidebound big-party voters to 
continue in their old mindset of "vote up my party, loathe the other big party, 
and pay no attention to any other party."
2. (Intertwined to reason #1) Elections shall, IMO, be occasions of public 
civics lessons. The voters should be forced to consider several different 
opinions, and no go reflexively party-list on every issue. By forcing voters to 
rank at least 4 alternatives, the voters would be forced to not only evaluate 
the other big party in relation to the minor parties, but also evaluate minor 
parties in relation to each other. That would force low-information voters to 
either throw away their vote, read up on policy positions, or random-rank their 
preferences #2 and below.

So, what would happen if a voting system with a BVP-criterion enforcement would 
be introduced? I see two possible scenarios:

1. The big parties split into several very similar parties, so that hidebound 
voters of that party can vote a complete list of only party members
2. The big parties do not split, and the voters of those parties engage in 
mutual burying. Their voters vote their party #1, then supply a long list of 
minor parties, so that they do not have to give any help to the hated other big 
party. Meanwhile, many 3rd party voters will vote one big party at the bottom, 
and several will tactically vote both big parties at #1 and #2 from the bottom. 

In the first case, the big parties run a risk of the different daughter parties 
becoming entities of their own, that become difficult to control. That is a 
good thing.

In the second case, the most centrist 3rd party will get a big boost, which is 
a good thing also. It is entirely possible that a new centrist party would be 
formed, peeling center-leaning voters off both present big parties. Then those 
big parties would become smaller, and with a much smaller span of political 
opinions within them, they would be more cohesive and we would get fewer 
intramural fights. All good IMO.

Peter Gustafsson                                          
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