Jesse Livermore stock selection strategy:

Jesse Livermore recommended buying shares which break out to new highs following consolidation, as he thought this is a sign of strong bullish momentum and no selling pressure. He would also pay attention to volume with such breakouts, seeking verification that there is buying pressure. This is part of his overall system of riding price trends, finding turning points (such as new highs), and pyramiding in successful positions.
The following is a more comprehensive explanation of Livermore’s strategy:
New Highs as Breakout Points:
Livermore viewed a stock’s making a new high as a major turning point, implying a breakout from a consolidation pattern.
Consolidation is everything:
The longer the consolidation period (sideways trading) prior to the breakout, the larger the ensuing move.
Volume Confirmation:
Livermore was particularly careful to watch the volume on a breakout. Strong buying on a new high indicates strong interest and validates the breakout as real.
No Overhang:
Livermore thought that stocks breaking out to new highs would have fewer short-term holders who would want to exit at breakeven prices compared to stocks declining from former highs.
Pyramiding:
If a stock had acted as expected after a new high breakout, Livermore would extend his position incrementally, building his way into the trade as it continued to work in his direction.
Trend Following:
Livermore made much of adhering to the trend of the market and stocks, rather than attempting to forecast the direction of the market.
Patience and Discipline:
He emphasized patience and discipline in waiting for the proper opportunities and adhering to his trading guidelines.