A Problem with (Almost) Universal Red Shift

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jaston
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It is my understanding that, except for a couple of local galaxies, everything in the universe is moving away from us as well as from each other (relationships between inhabitants of local galactic groups excepted). If my information is acurate, how is it that a large collection of randomly placed objects could possibly act in that way? Wouldn't some of them have to be moving toward us?

I ask because the only way that makes sense to me is if all super massive objects/groups in the universe are actually motionless and the spacetime between them is expanding. Any motion at all from them would, in some direction, be read as a blue shift and just by the strength of numbers, some of those blue shifts would be pointing in our direction.
 
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I believe (not really sure) that distant galaxies DO have a local motion that is random relative to their direction to earth, BUT this motion is utterly trivial relative to the "motion" we see due to expansion.
 
Sure, there are variations where some have more motion towards us than others do, but as you get further and further away the average redshift steadily increases.