Round Robin Quilts are quilts made by individuals taking turns on each other's medallions by adding rows to the outside, or in some cases, just adding horizontal rows. They're all good fun.

I've been looking around the web today to show examples some of our quilt friends are doing. A Medallion Quilt made by one person may be called a Round Robin Quilt if she waits until one section is done before planning another. It can be a fun game of solitaire, or one can join only a group that decides on a plan. For example, a group of quilters who are new to quilting would be wise to stick to tried and true methods, whereas a group of artists might specify that round one is piecing, round 2 is applique, colors used are (fill in the blank), or no rules at all if the quilters are on a par with oneself. Advanced quilters are likely to feel disgusted when they spent 40 hours doing their rounds, and the next quilter sewed 4 solid pieces of unadorned fabric, slightly off from the rest of the quilt as her "contribution" which took all of 20 minutes.
Here are some I found that are similar to what a group of round robin quilters in my quilt shop's area did in years past:
So you don't really know what the end result will be until it is finished?
If you are working in a group and you have good partners, you're going to like it. If you do it on your own, you're likely to like it. If you're working with a group of beginners, buy an extra ripper.
I'm not sure that exactly answers your question, but honestly, I only worked with one group who only worked with me because I had the best selection in the state, being an artist devoted to having a plethora of hues, shades, tints, southwestern atmospherics, character, birds, western, and nature choices from the best suppliers. They were jet setters, and their works were astonishing. Each one made certain after her round was done, it was a master work. They stayed together for years and were devoted to each other's families as well as each other's artistic likes and charitable activities. Any of them could have been CEOs, but they chose domesticity over careers. Their common ground was aesthetic excellence.
Last night, a small stack of oranges and a yellow that looked ok with the yellow already on the quilt (of which none could be found), plus a black and white print that halfway reflected the black and white dot around the butterfly, too. This morning, the quilt was remeasured and measured a little over 21.5 by 33". 21 and 33 are both divisible by 3, and a little trimming or ooching and scooching (which can be done with cotton with no ill result) could make a rather nice 3" border, but there was only enough black and white to cut 1.5" strips from two pieces, enough to make 48 Roman stripe squares all the way around, with black and white being on either side and the main contrast to the solid light bright orange on the outer row.
Starting with a finite, squared center is not always what it's cracked up to be. One may not remember the measurement from 3 years ago that it took to attain a pleasing balance of positive and negative spaces, which are best ordered, plus a quilter always has to have a little bit more with the 1/4" seam allowances that must be taken away.
This is a case for not getting too wrapped up in preplanning, because different quilt artists have different requirements, and often those requirements change from work to work. It's a lot of math.
So it was math that basically drove the choice for the roman stripe idea--the number of inches of 45" fabric that could be parsed into something that would come out 3x3 all the way around the quilt, in odd numbers (which couldn't have been better). It was the good fortune of having black and whites separated from other fabrics that presented two of the same print purchased at different times, and used along the way for creating other stripped projects. The piece picked would never have been my choice consciously, because it splits black and white evenly, which places it in the "average" value category. But its use of an unusual-looking dispersive background along with a vining floral throughout was frenetic enough to satisfy a subjectively pleasing diversity, imho.
This was what it looked like, and when placed next to the quilt had the unexpected fun look of huge running stitches all around. It just jazzed me, that's all.
Scan 1 - Strip to go along sides
Scan 2 - Strip to go along top and bottom
Scan 3 - Strips overlapped to show juncture (sorry one of them slipped a little)