Cut large potatoes into quarters and cut small potatoes in half. Place potatoes into a large stockpot and enough water that the potatoes are covered by at least an inch. Bring the pot to a boil then reduce heat to medium and maintain a simmer. Cook the potatoes for about 15-20 minutes, or until fork tender.
Once the potatoes are done cooking, drain off the water and rinse with cold water to stop the cooking process. Place the potatoes in the refrigerator until they’re cool enough to handle.
Meanwhile, whisk together the mayonnaise, mustard, pickle relish, pickle juice, paprika, salt and pepper.
Once the potatoes have slightly cooled, remove the loose peels and chop the potatoes into ½ inch chunks. Place the potatoes in a large bowl and add the hard boiled eggs, radishes, celery, onion, and mayonnaise dressing. Gently mix together until the potatoes are well coated with the dressing.
Cover and refrigerate for 2-3 hours or overnight. If desired, garnish with additional diced radish, celery, and chives and sprinkle with paprika before serving.