Performing "mostly within" selection using ArcMap?

While I think you could do with refining your question with a bit more detail (how much of the line has to be within to qualify, how do you want to handle lines coincident with polygon edges, etc... I do have a thought on generally how you might be able to approach this problem. Yes, this would be a relatively elaboarate method to accomplish what should be pretty easy to do, but... it should work none-the less. One way would be to build a model or script that would use a GP tool to split all of your line segments at the polygon boundary (I would probably do this with clip tool using a layer with selection applied for the polygon to clip by so it only uses the polygon(s) in question. If you have the output of that tool go to a geodatabase and you have your initial dataset in a geodatabase, then you would just have to do a table to table join on the two line files (original and output of GP tool) and then calculate the percentage difference between the two Shape.Len fields (if a line segment in original file is 100 ft long, and that same line segment, clipped to the polygon, is 75ft long, then 75% of that line would be within the polygon). Then you could just do a select by attribute based on this percent.

Again, I know this is rather involved, it creates an intermediary dataset, and there probably is an easier way to do this that I don't know about; but, if you write a model or script to do such, and delete the output line FC when you're done with it, it shouldn't appear all that difficult to the end user... even if it's a bit of a pain to build initially.

Just some thoughts, and let me know if that doesn't make sense and I'll try and explain better.

Based on the responses I received here, I used a combination of ideas provided.

First what I did was add a Length and Percent field to my original dataset. I copied the Shape.Length values into the Length field.

Secondly, instead of using Clip, which is significantly more work in this case, I used the Intersect tool. This "clips" the polylines that intersect the polygons and adds in some potentially valuable attributes. Despite having a truly unique ID field, I don't think its really required when using a static length field.

Finally, I just simply calculate the percent of the difference between the new Shape.Length and the static Length field to the Percent field. Any polylines that intersected the polygon boundary will have a percentage less than 100.

1. Split the polyline at each vertex,
2. for each segment call completely within on the end points,
3. any segment that is completely within has 100% of its length within the polygon, (assuming no re-entrant polygons), and its length can be added to a total,
4. any partial lines can be split into say 10 segments and the same calculation applied.
5. Compare the total with the length calculated to get a resolution of 10%, (if you need more accurate results then you can sub-divide finer on the partial lines).
6. You could even keep a total of the lengths of the totally outside lines as well and only do the partial line calculation only if you have neither answer past your threshold.