In a large serving bowl, combine the drained blackeye peas, corn, jicama, cucumbers, bell peppers, onion, cilantro and jalapeño.
In a small bowl, whisk together the dressing ingredients: olive oil, sugar, white vinegar, red chili pepper, cumin, and lime juice. Drizzle the dressing over the serving bowl and toss until well mixed.
Season to taste with additional salt and pepper.
For best flavor, let the mixture marinate for at least 20 minutes before serving. Serve as a salad or a dip with chips.