[EM] Woodall Tests (was Realism of Tideman vs Schulze numerical testing)

[DEMOREP1 at aol.com]

there is a paper by Woodall in which he demonstrates that
no preferential single-winner election method can meet the
following four properties simultaneously [Douglas R. Woodall,
"An impossibility theorem for electoral systems," Discrete
Mathematics, vol. 66, p. 209-211, 1987]:

1) monotonicity;

2) later-no-help and later-no-harm;

3) if no second preferences are expressed and candidate A
   has a plurality of first preferences, then candidate A
   must be elected;

4) if more than half of the voters strictly prefer candidate
   A and candidate B to every other candidate, then either
   candidate A or candidate B must be elected.

Which of Woodall's properties would you be prepared to see
not satisfied by your preferred system?
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D- How many of such tests relate to YES/NO, head to head and/or place votes 
tables ???

Test 3) fails simple majority rule.
Test 4) seems to be a variant of YES majority votes.