autochange and multiple voices

[Jérôme Plût]

Consider the following score:
\new PianoStaff <<
  \new Staff = "up" {
  <> % this should do nothing...
  <<
    \new Voice \relative { e''4 f e }
    \new Voice \autochange \relative { a'~ a g }
    \new Voice \autochange \relative { c'~ c b }
  >> }
  \new Staff = "down" { \clef F <<
    \new Voice \relative { a d, e }
  >> }
>>


Problem 1: why, on the third beat, is the alto voice (playing a g')
displayed on the "down" Staff?

Problem 2: delete the line saying "<>" and recompile. Now
all hell breaks loose: the score acquires a third staff, which even
eats the soprano on the third beat...
(on the other hand, the chords on beats 1 and 2 are now nicer).
Why? (I guess that the "up" Staff had a default, empty voice
through the "<>" - is that correct? but it does not explain all).